https://sayyari.netlify.app/courses/math162m/lectures/period-1/Recent content in Period 1: Solving Quadratic Equations on Sayyari: PreCalcIHugoen© 2023 Dr. Mohammed Sayyari -- Based on notes by Lisa Blumhttps://sayyari.netlify.app/courses/math162m/lectures/period-1/1-quadratic-equations/Mon, 01 Jan 0001 00:00:00 +0000https://sayyari.netlify.app/courses/math162m/lectures/period-1/1-quadratic-equations/<p>This document may contain unfilled definitions or examples. We will go over these during the class and the filled version will be posted after the lecture. <button type="button" onclick="toggleAll(this)">Reveal all answers</button></p> <h1 id="quadratic-equations">Quadratic Equations<a class="anchor" href="#quadratic-equations"></a></h1> <h2 id="quadratic-equations-in-standard-form">Quadratic Equations in Standard Form<a class="anchor" href="#quadratic-equations-in-standard-form"></a></h2> <h3 id="definition-quadratic-equation-in-standard-form">Definition: Quadratic Equation in Standard Form<a class="anchor" href="#definition-quadratic-equation-in-standard-form"></a></h3> <p>A quadratic equation in standard form is written as:</p> <p><span class="blank" id="blank1">___________</span> <span id="answer1" style="display:none;"><span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">ax^{2} + bx + c = 0</annotation></semantics></math></span></span> <button id="btn1" onclick="reveal('blank1', 'answer1', 'btn1')">Reveal</button></p> <p>where <span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><link rel="stylesheet" href="https://sayyari.netlify.app/courses/math162m/katex/katex.min.css" />, <span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span>, and <span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi></mrow><annotation encoding="application/x-tex">c</annotation></semantics></math></span> are <span class="blank" id="blank2">___________________</span> <span id="answer2" style="display:none;">real numbers</span> <button id="btn2" onclick="reveal('blank2', 'answer2', 'btn2')">Reveal</button> and <span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo mathvariant="normal">≠</mo></mrow><annotation encoding="application/x-tex">a \neq</annotation></semantics></math></span> <span class="blank" id="blank3">___________</span> <span id="answer3" style="display:none;"><span class="katex"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span></span> <button id="btn3" onclick="reveal('blank3', 'answer3', 'btn3')">Reveal</button>.</p>