{"id":510,"date":"2026-05-12T20:47:33","date_gmt":"2026-05-12T10:47:33","guid":{"rendered":"https:\/\/www.the-bach.kiwi\/?p=510"},"modified":"2026-05-12T20:47:34","modified_gmt":"2026-05-12T10:47:34","slug":"year-10-quadratic-equations-revision-discussion-page","status":"publish","type":"post","link":"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/","title":{"rendered":"YEAR 10 QUADRATIC EQUATIONS \u2014 REVISION &#038; DISCUSSION PAGE"},"content":{"rendered":"\n<p>Based on your uploaded chapter on quadratic equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">1. What is a Quadratic Equation?<\/h1>\n\n\n\n<p>A quadratic equation has the form:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre> ax^2 + bx + c = 0<\/pre><\/div>\n\n\n\n<p> ax^2 + bx + c = 0<br><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a, b, c) are numbers<\/li>\n\n\n\n<li>(a \u2260 0)<\/li>\n<\/ul>\n\n\n\n<p>Examples:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 + 5x - 6 = 0<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2x^2 - 7x + 3 = 0<\/pre><\/div>\n\n\n\n<p><br><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">2. Why Quadratics Matter<\/h1>\n\n\n\n<p>Quadratics model:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>ball trajectories<\/li>\n\n\n\n<li>arches<\/li>\n\n\n\n<li>bridges<\/li>\n\n\n\n<li>jumping\/diving paths<\/li>\n\n\n\n<li>maximum heights<\/li>\n\n\n\n<li>area problems<\/li>\n<\/ul>\n\n\n\n<p>The chapter overview discusses real-world uses including sports, architecture and satellite dishes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">3. The Shape \u2014 The Parabola<\/h1>\n\n\n\n<p>Quadratics graph as a parabola.<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Positive-a\" >Positive (a)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Negative-a\" >Negative (a)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Core-Idea\" >Core Idea<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Simple-Trinomial\" >Simple Trinomial<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Difference-of-Squares\" >Difference of Squares<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Example-Structure\" >Example Structure<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Example\" >Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Forgetting\" >Forgetting:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Quadratic-Formula\" >Quadratic Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/#Discriminant\" >Discriminant<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Positive-a\"><\/span>Positive (a)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Parabola opens upward.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/xE1M-m_XBnwpRm9NqzWo4ScFRllHmbX5fVb_oMvLxisQ2jsHSK5dZscQ4Rau9xu_AnzqCaz2BWkZjE_m5rZBQwNwSuAMR1z0CNL_gPyeQGN5FMomiv1MC0VDPtILLiPAfIcV05IEEKI9Zxicyg32yni88AKF-rgVo3dgYFk22Uxm0XKRDScj4hL-4qBOZHlT?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/ldEqG6oDK5hjhrYx5xcSiMu9Ji9mBXd3nEvJI9Tt0lYfHT9MZYAKZevu4qGAxuC-OjYpOWuDSNpegFO6a_wYPHc-kYEcMSHeVkSW80c71aihJslOIniVQ_l6gDdoOglpDrq_0XdCQ7xGa1RDDxdhwPPQ41v3PxAk1ICcIusG-WiSJ_8r5b1xi3FOfDUIWM9m?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/76JysSuXulxGEL25a69llp4J95pt_Iq6TW6856TJq5da7G1S-S9oMzs4fsVLVIaVUj1dtah3DtNmXGs7x_oEf5HPbptL94KjY9dtw1WL8CaLLWqaVhGy0N_Lk1UZbSIxx5Fr66Py-EzoXrhL96DOkW4wyFUfHWKzSeb_oFSa0N7SENYdTrtYEnMKoiuu-CIh?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/7yb2tBWmRm3vx-JXB9i6cJAvtzZCXWtnOemVejqLVYsyO_XSghW93nbBXEIG8kWwt0sf3NL40EaNQetWEbe4z3ZVHj3tY__05SbdlEyVQvvPkzaFDAfyzb6phklrII-3NZqc0FGc9XlCfJ39C4jK9Fp_5GND9xDHU2FU8xL5hmoif-g9QkgywjNluBboHZEt?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/fUwA0AGbjHXjqK9pisnsxuoaPhd3OB4Li2lyB7QPWiN6d7lqdqCUL14hBD3aiEudU9z293kwAODmZfjhFLlDx1ytuMp6xa_mHoQCUjj2V4nChvRBFpY6Oh5nndQ1Igf3nkaR6rLGCLHiy3sb_K9E459If2N6KlrDXD7vKIwrUF0CUiOXB2mbyxd5zVuboisz?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/qWKgFc5no0Ydndfna7GhoCi1Ns_9jfmstgLG45bW3G9PNQsQOLXtZ3ZH9VIkprAPX7vCph-ZVTV8bB0CwC8zKcPdearDM0L83ODkddDQrN4ypMf2QuiYD5syF50wQV-za4Lij1RHn3Es6VHbHjDxAKPjVMQ9OBbgYgBLpFLzT9WSVlJePWRPli2kNiQX8oPR?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Negative-a\"><\/span>Negative (a)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Parabola opens downward.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/BYRoHSZi7d1dOiTLwYRFtdataK_fu7XQd_fhxBVAexlpcLRzusinGYMnRyq1G_CqHwlONWTD5rYqM4DsrrvSsj9NGlP18MlfzIFT1ToSZO94d12dlfax8VZ9eI3ZLXKyuWXDrPX4xrCTE9UUC2kAbyS5EhdZN02VTa_jaYgB_xMH_XYZmqylMHtWLR6S-3k4?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/GRDnmQkO_gWPhvA6nNpNBkapQX81GlexWWADLNauQ9Ju6zy8l4_jnGWnw3-y5Gg-BDTg6JdwmRk-6sEUV8yheq63wLD3y__qXKxuMJQPtgCBKGPtv_D9VfBkf7lhLQC0INsiC0zIim4fM-s-K-Xhi3mtFB5p9hgBIeDSp4nRefIMNag1tk00jQS_Iy1Q5SYA?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/N4M7OxnIx6ZWtO_05U2Iix5SY7ZcFNJF7Z6seCGxz8rNKytkGajNfATHNSyY1gXsAGW7g45twfN1FCTIDlh81o9WHmEQPdGaHj6edmakyppfvjAKtELVC4dS9Fb8LpVM_j1oYeGgks4T3SWJUxRNc79qDaBULkeaaJxrv6SLjEQ-_wQDGkP8Z8aeUsYEc9Ng?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/efCCSDnNAKAdY6ZXo3WYS0qiHESnaiO5J5K_Q1PVFqCqPvgTf0oG-3te1VDbr3tjzHZYAvrU0-BEye-vNJSleL2CBRbdAJK2VYkTo61whGw8GAwrYQV1nSthqjptE0_SWt3E10TURAzNDtjVbkQLa9B-STQAHajCKoJraOyUe_ln-Pbf8TSyxhjEYjMu12y5?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/W9uCwaIdNNUA-5cWOZlxGLGl95pn3YU72PflI28n7TTHJktMn254UDTTKUl1RNt3Axo4iVY962JJ4RY67koCHG2hjufssu8pfEDh5QRLErgWwcG9x66nPNEooHwxoXovUaMg-3E2ZqcwmQdtA4UYnCG7XLhlR-gwAuVgHFvU7jz76cTA4Akyw2wHgZs6MVpj?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/sLktnddIXoOtKS-AZn_ACmhV_qNkRTAg5XF4XGFpyTK7VJ-cVic97aI4YSPvTAIdWaJKZiwvHON0k8nZgPO4PaRshb9vTHxBQhIXPLLogkCIn8GG7SzuOXWCl9opwKQZS4csyTSjJwWe7T0k6hLWzCBXl6NE0RLNg5nqlKhjvHC8nlZTCg9_RiXjuiTsG8yI?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">4. Solving by Factorising<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Core-Idea\"><\/span>Core Idea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>If:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(x - 3)(x + 2) = 0<\/pre><\/div>\n\n\n\n<p>then:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x - 3 = 0\n\\quad \\text{or} \\quad\nx + 2 = 0<\/pre><\/div>\n\n\n\n<p>So:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x = 3\n\\quad \\text{or} \\quad\nx = -2<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">The Null Factor Law<\/h1>\n\n\n\n<p>If two numbers multiply to make zero:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>ab = 0<\/pre><\/div>\n\n\n\n<p>then:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a = 0\n\\quad \\text{or} \\quad\nb = 0<\/pre><\/div>\n\n\n\n<p>This is the MOST IMPORTANT algebra rule in factorising quadratics.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">5. Factorising Patterns<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Simple-Trinomial\"><\/span>Simple Trinomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 + 5x + 6 = (x + 2)(x + 3)<\/pre><\/div>\n\n\n\n<p>Find:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>two numbers multiplying to (+6)<\/li>\n\n\n\n<li>adding to (+5)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Difference-of-Squares\"><\/span>Difference of Squares<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 - 25 = (x - 5)(x + 5)<\/pre><\/div>\n\n\n\n<p>Pattern:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a^2 - b^2 = (a - b)(a + b)<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">6. Solving Using the Quadratic Formula<\/h1>\n\n\n\n<p>When factorising is hard, use:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}<\/pre><\/div>\n\n\n\n<p>The textbook introduces this in Lesson 8.3.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Example<\/h1>\n\n\n\n<p>Solve:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 - 5x + 6 = 0<\/pre><\/div>\n\n\n\n<p>Identify:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a = 1)<\/li>\n\n\n\n<li>(b = -5)<\/li>\n\n\n\n<li>(c = 6)<\/li>\n<\/ul>\n\n\n\n<p>Substitute carefully.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">7. The Discriminant<\/h1>\n\n\n\n<p>The discriminant is:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\Delta = b^2 - 4ac<\/pre><\/div>\n\n\n\n<p>It tells us HOW MANY solutions exist.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Discriminant Summary<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Discriminant<\/th><th>Meaning<\/th><\/tr><\/thead><tbody><tr><td>( \u0394 > 0 )<\/td><td>Two solutions<\/td><\/tr><tr><td>( \u0394 = 0 )<\/td><td>One solution<\/td><\/tr><tr><td>( \u0394 &lt; 0 )<\/td><td>No real solutions<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>From Lesson 8.5.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Visual Meaning<\/h1>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/1VQkTPDSmLlu8eA82czfZLuivEVj1xdYY9lbp-GG7dKjCbiD4ai2evXemEDz3fKqZbomEpdLge-rQ0gTYn-PnZjM5_yyy-YAXdwen_LXb3rw6SzU_3DER83VRSrY9ab7-NXyON2hUNCAPcnMH2JbCyzQSVkiD82BDmVYbt5KxfeWID9ncGEzZClF_nJP3p0O?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/Q2OtRTq4xburws6qn-wmgF1taiZjn4vwtF16SYg67MtpCcPP5AiSvDA0nQkarbzZVqlRq5hrxFiQM80nHIsUKDs_loVcp2uO0Q79j3VZiMjy2lhcVR0hOlQzUWwr_TvXeNrVzgV1CDo-_nBnE32B7JjF8y-syLvBfJeKMpkExKn6swXIYCCKxN47OPrLkwh8?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/0cxeslLewA32yqDC3PGpyPZnxEgSMD3Pcr3HBNQJg509TiAIzFQHuzcdg-_Wb2N_ue5ZB0X4Ijl-QNIvD14tg39emwmItUSoyGGfSsQCE8wxwaL0gLKs8cw6Imw19EYzP0gWK6BRrbm66NPn-rjgCSGb5i9EugKQrcXkQQpV-OOrMYA43WetELPJJ_RXIHZa?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/liiRdcFOEiDwsMEeyWZc0ukfHFXPXc2n6qSDQUwBhNw6Kq9l-At8okWWCGbGAvxEPHDFeHJTQSw-oH1c1ZOpE7lFf_MqKLcHJBd8FV9s34KF6N4Q-I4GvA-6kD2SQ8zscAWdDJm1IazTQj-Unewvyop-IcT7Zz1Q9rOdwNhg9P6d9Mf3Xt6n1v1ykx-DY11T?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/S6SY-YJLWZ85KGjr84HCdBXRzuL1EB1L9m3Q7MiCaLP97VCx3ITBWQG4AsBcspXhgSTfo9piXPPyOQSRbixetPSvp_6UkzxKumGwspe8Fo77bFiXXxUZZpvjLL6f98oVxDNBSojteld5wME2xrtRrOEyNEesdy8Grf2SCoYMT99mUL6KU8lCSZuea5NQzkZ_?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/gAW8dQElSre60hl4UF4lizUKjnxyueZ4gVPqdOFPTBs7Zd2lp6STZLjKQmfJtY4452cCWsAmTMhv5W5motF2FJwFIH8mKf08ovbkndIZEaM16JA5P28dM3MbxRv5VE8ellRdDtAym90h4xmrEmdHtWuvvqBEEOZK2xuQyygt_ohHzzHG_w68xZO6LcKTb34b?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Crosses x-axis twice \u2192 2 solutions<\/li>\n\n\n\n<li>Touches once \u2192 1 solution<\/li>\n\n\n\n<li>Misses x-axis \u2192 no real solutions<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">8. Solving Graphically<\/h1>\n\n\n\n<p>Solutions are where the graph crosses the x-axis.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/hLIobR91C7qvzz_qRFw_9eHXKYrTwEd9j-0Q8dmtG-Kwa7IC9c8q7fSUlu90p5inJQUL4FhEUytJrrZLjzGyNvX-y_fNOyAlfRgpZOUkvuD6oSom8mEFeLFqTdIsqeCKUiS2NgXnPLFb20BKWUfGxLAKOczOUOojZbYsAl4VzByq9DSeb7sLRw5FLHNVEKEA?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/k-XSI_NXqLlQIaw5T0FL3RZfaaNll5O-DoF08NLu-EfyeVSZ56IV6uUP0bJeSvHxT03JU9YAJgQBSp-HvoT9C7Nfzb0rlT6OQmmhbllD4q-018zjXhhniZ4z46c60vi7VgxURa8RKb8TMWGOPOYuCKWA_wJ0aD_B5J7AAjGDP0krjcng8Cz8gHQABJPXXxKm?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/jaUptzzLaZHxJHcWZxAMd2FyNz00vrYNVGL9llDq9iaHIcGhdYFtzZtW0ZgAcPN1gYo4Fwm6uKu1WX-Ghs0gNrxiyYXCbgypIj64WA4O-hHUqstDPb8QugzvOdwmJJkplqKGZmgiH3hM896hrVF_IX5id-oMyDRAQnhq96p-R0EQyNVlLjIgJgX08r4rVaLx?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/dLOzYLGR65Wa6Vcyv-iiLInbZ9U6kuIVIVH5IUXWeSaJ5K4l5zbz_OB0pk-N7FemjZgFVop7-Bazovo94-uE4A06xyjD1FC6lnMknwu8vNa5yrMF4S7aCi6KqwzejjH69X_bS6rWC7R5Rp-feQ5WoUzBDun8_1wMthVdhFCmWSlXldRg1YoV2-Vdi7cJXLoT?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/vpNyoI22CmeemLi7g6KKQpvSGRKDbOku_8c9j0DghMdDFSMsWNAiJzl8UCrt0iQHmz1HCb-QqnbJWdffCCpSjm9tvG5pnRkFEMiBbUpQ9HMOTwXByYXQrIwoEdz6lLShYOzVIUYG3Oh3UM0gLo1eG0y3Xh-PxWKX9lWZZOAkb0AUUyUD3tZO_Gdr6SNqN6v2?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/images.openai.com\/static-rsc-4\/cwrrZ_C1UrMd03fvMQ4B3-glZoO3zN019A9NZC8kYx2qNpvtPTFu8sc0f9jYD2po0dFQ3pwSEwAvGyxhOhHQ4A5RbjnQqq2FVdOF_QbvD9CEkkugD1t8bX6MOfYSyu6Ja0ZAUmp0oOcKCZdeC9J53vprwuxriS57wgn9ESeKWTNoZenjmPo4CP4c6svhODa7?purpose=fullsize\" alt=\"Image\"\/><\/figure>\n\n\n\n<p>Example:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>y = x^2 + x - 2<\/pre><\/div>\n\n\n\n<p>Solutions:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x = 1\n\\quad \\text{and} \\quad\nx = -2<\/pre><\/div>\n\n\n\n<p>The textbook explains that the x-intercepts are the solutions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">9. Completing the Square<\/h1>\n\n\n\n<p>Used when factorising is difficult.<\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 + 6x + 2 = 0<\/pre><\/div>\n\n\n\n<p>Add and subtract:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\left(\\frac{6}{2}\\right)^2 = 9<\/pre><\/div>\n\n\n\n<p>So:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 + 6x + 9 - 7 = 0<\/pre><\/div>\n\n\n\n<p>Factorise:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(x + 3)^2 - 7 = 0<\/pre><\/div>\n\n\n\n<p>Then solve.<\/p>\n\n\n\n<p>The textbook explains this process in Lesson 8.2.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">10. Worded Problems<\/h1>\n\n\n\n<p>Typical Year 10 applications:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>area<\/li>\n\n\n\n<li>projectile motion<\/li>\n\n\n\n<li>dimensions<\/li>\n\n\n\n<li>consecutive numbers<\/li>\n\n\n\n<li>geometry<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Example-Structure\"><\/span>Example Structure<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Define variable<\/li>\n\n\n\n<li>Build equation<\/li>\n\n\n\n<li>Rearrange to zero<\/li>\n\n\n\n<li>Solve<\/li>\n\n\n\n<li>Check answer<\/li>\n\n\n\n<li>Write sentence with units<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Example\"><\/span>Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Two consecutive numbers multiply to make (20).<\/p>\n\n\n\n<p>Let first number be:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><em>x<\/em><\/p>\n\n\n\n<p>Second number:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><em>x + 1<\/em><\/p>\n\n\n\n<p>Equation:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x(x + 1) = 20<\/pre><\/div>\n\n\n\n<p>Expand:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x^2 + x - 20 = 0<\/pre><\/div>\n\n\n\n<p>Factorise:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(x + 5)(x - 4) = 0<\/pre><\/div>\n\n\n\n<p>Solutions:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x = -5\n\\quad \\text{or} \\quad\nx = 4<\/pre><\/div>\n\n\n\n<p>So the pairs are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>((-5, -4))<\/li>\n\n\n\n<li>((4, 5))<\/li>\n<\/ul>\n\n\n\n<p>Based on Worked Example 4.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">11. Common Exam Mistakes<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Forgetting\"><\/span>Forgetting:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>to rearrange equation to (=0)<\/li>\n\n\n\n<li>negative signs<\/li>\n\n\n\n<li>both solutions<\/li>\n\n\n\n<li>brackets<\/li>\n\n\n\n<li>square roots<\/li>\n\n\n\n<li>checking factor pairs<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">12. High Value Exam Questions<\/h1>\n\n\n\n<p>You should be able to:<\/p>\n\n\n\n<p>\u2705 Factorise quadratics<br>\u2705 Use Null Factor Law<br>\u2705 Use quadratic formula<br>\u2705 Solve graphically<br>\u2705 Use discriminant<br>\u2705 Solve worded problems<br>\u2705 Interpret graphs<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">13. Memory Tricks<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Quadratic-Formula\"><\/span>Quadratic Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u201cMinus b, plus or minus square root\u2026\u201d<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Discriminant\"><\/span>Discriminant<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Positive \u2192 2 solutions<br>Zero \u2192 1 solution<br>Negative \u2192 none<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">14. Essential Summary<\/h1>\n\n\n\n<p>Quadratics are about:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>curved relationships<\/li>\n\n\n\n<li>solving for unknowns<\/li>\n\n\n\n<li>graph behaviour<\/li>\n\n\n\n<li>real-world motion and area<\/li>\n<\/ul>\n\n\n\n<p>The four BIG skills are:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Factorising<\/li>\n\n\n\n<li>Quadratic Formula<\/li>\n\n\n\n<li>Graphs<\/li>\n\n\n\n<li>Discriminant<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Useful worked examples, exercises and graphs appear throughout your uploaded chapter.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Based on your uploaded chapter on quadratic equations. 1. What is a Quadratic Equation? A quadratic equation has the form: ax^2 + bx + c = 0 Where: Examples: 2. Why Quadratics Matter Quadratics model: The chapter overview discusses real-world uses including sports, architecture and satellite dishes. 3. The Shape \u2014 The Parabola Quadratics graph &#8230; <a title=\"YEAR 10 QUADRATIC EQUATIONS \u2014 REVISION &#038; DISCUSSION PAGE\" class=\"read-more\" href=\"https:\/\/www.the-bach.kiwi\/index.php\/2026\/05\/12\/year-10-quadratic-equations-revision-discussion-page\/\" aria-label=\"Read more about YEAR 10 QUADRATIC EQUATIONS \u2014 REVISION &#038; DISCUSSION PAGE\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-510","post","type-post","status-publish","format-standard","hentry","category-uncategorised"],"_links":{"self":[{"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/posts\/510","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/comments?post=510"}],"version-history":[{"count":1,"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/posts\/510\/revisions"}],"predecessor-version":[{"id":512,"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/posts\/510\/revisions\/512"}],"wp:attachment":[{"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/media?parent=510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/categories?post=510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.the-bach.kiwi\/index.php\/wp-json\/wp\/v2\/tags?post=510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}