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authoraltaf-creator <athaalaa@gmail.com>2023-09-25 06:13:47 +0700
committeraltaf-creator <athaalaa@gmail.com>2023-09-25 06:13:47 +0700
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+<!DOCTYPE html>
+<html lang="en">
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+ <title>Al Azhar 9th Grade Lesson Notes</title>
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+ <img src="/assets/images/master.svg" alt="" class="sidebar-logo">
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+
+ <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3>
+ </div>
+
+ <div>
+ <a href="/about/author.html" class="sidebar-link link">About the Author</a>
+ <a href="/about/school.html" class="sidebar-link link">About School</a>
+ <a href="/lessons" class="sidebar-link link">Lessons</a>
+
+
+ <hr class="divider">
+ <div id="toc">
+ <h4>Table of Contents</h4>
+ </div>
+ </div>
+ </div>
+
+ <div class="banner-container" id="banner">
+ <div class="banner-bg" id="img-supplies"></div>
+ <div class="gradient-bg"></div>
+ <div class="banner-text-container">
+ <h1 class="banner-text" id="banner-txt">Quadratic Equation: The Introduction</h1>
+ <h3 class="banner-text" id="banner-txt">Chapter 2</h3>
+ </div>
+ </div>
+
+ <div class="chip-container" id="chip-container">
+ <div class="chip" title="Beware of mistakes. Please report to me (Altaf) if you caught a mistake here."><span>❓ Unchecked by Professionals</span></div>
+ </div>
+
+ <div id="main">
+ <section>
+ <h1 id="introduction">Introduction</h1>
+ In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x
+ represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.<sup>[<a
+ href="#reference-1" class="link-compact">1</a>]</sup>
+ <h2 id="introduction--formula">Formula / Format</h2>
+ <span class="math-font">ax<sup>2</sup> + bx + c = 0</span>
+ <p>
+ <span class="math-font">a, b, c</span> = known numbers, where a &NotEqual; 0 <br>
+ <span class="math-font">x</span> = the unknown, or the root
+ </p>
+ <h2 id="introduction--exercise">Exercises</h2>
+ <h3>Finding the roots with factorisation.</h3>
+ <ol>
+ <li>
+ <span id="q1.1.1"></span>
+ <p>
+ <hr>
+ <span>To find the answer, we need to find the factors of c that is suitable for b and c. <a href="finding-suitable.html" class="link">What and how do I find the suitable factors?</a></span><br>
+ <span>The suitable factor for the equation are <b>2 and -3</b>. </span><br>
+ <span>Then, insert each numbers to this formula: <span id="q1.1.2"></span>, where <span
+ class="math-font">y</span> is the factor.</span><br><br>
+ <span id="q1.1.3"></span><br><span id="q1.1.31"></span><br>
+ <hr>
+ <strong>So, the answer is <span id="q1.1.4"></span></strong>
+ </p>
+ <script defer>
+ var element1 = document.getElementById("q1.1.1");
+ var element2 = document.getElementById("q1.1.2");
+ var element3 = document.getElementById("q1.1.3");
+ var element31 = document.getElementById("q1.1.31");
+ var element4 = document.getElementById("q1.1.4");
+
+ katex.render(String.raw`x^2 - 1x - 6 = 0`, element1, {
+ throwOnError: false
+ });
+ katex.render(String.raw`x + y`, element2, {
+ throwOnError: false
+ });
+ katex.render(String.raw`
+ \begin{aligned}
+ x + 2 &= 0\\
+ x &= -2\\
+ \end{aligned}
+ `, element3, {
+ throwOnError: true
+ }); katex.render(String.raw`
+ \begin{aligned}
+ x - 3 &= 0\\
+ x &= 3
+ \end{aligned}
+ `, element31, {
+ throwOnError: true
+ });
+ katex.render(String.raw`x = \{-2, 3\}`, element4, {
+ throwOnError: false
+ });
+ </script>
+ </li>
+ <li>
+ <p>
+ <span id="q1.2.1"></span><br>
+ <span><strong>Factors:</strong> <span class="math-font">2, 4</span></span><br>
+ <hr>
+ <span id="q1.2.2"></span><br>
+ <span id="q1.2.3"></span><br>
+ <hr>
+ <span id="q1.2.4"></span><br>
+ </p>
+ <script defer>
+ var element1 = document.getElementById("q1.2.1");
+ var element2 = document.getElementById("q1.2.2");
+ var element3 = document.getElementById("q1.2.3");
+ var element4 = document.getElementById("q1.2.4");
+
+ katex.render(String.raw`x^2 + 6x + 8 = 0`, element1, {
+ throwOnError: false
+ });
+ katex.render(String.raw`
+ \begin{aligned}
+ x + 2 &= 0\\
+ x &= -2\\
+ \end{aligned}
+ `, element2, {
+ throwOnError: true
+ }); katex.render(String.raw`
+ \begin{aligned}
+ x + 4 &= 0\\
+ x &= 4
+ \end{aligned}
+ `, element3, {
+ throwOnError: true
+ });
+ katex.render(String.raw`x = \{-2, -4\}`, element4, {
+ throwOnError: false
+ });
+ </script>
+ </li>
+ </ol>
+ <h1 id="relation-algebra">Relation between Quadratic Equation and Algebraic Expressions</h1>
+ <p>This is an algebraic expression &rightarrow; <span id="m0"></span>. You can turn that into a quadratic equation.</p>
+ <span id="m1"></span>
+ <script>
+ const m0 = document.getElementById("m0");
+ const m1 = document.getElementById("m1");
+
+ katex.render(String.raw`(x + 5)(x + 7)`, m0, {
+ throwOnError: false
+ });
+ katex.render(String.raw`
+ \begin{aligned}
+ (x + 5)(x + 7) &= x^2 + 5x + 7x + 35&\\
+ &= x^2 + 12x + 35&\larr\textnormal{quadratic equation 😱😱}
+ \end{aligned}
+ `, m1, {
+ throwOnError: true
+ });
+ </script>
+ <h1 id="all-about-roots">Quadratic Equation's Root Operations</h1>
+ <h2 id="finding-qe">Finding Quadratic Equation with Roots</h2>
+ <p>You can use the formula below to find a Quadratic Equation with 2 roots.</p>
+ <span id="m2"></span><span>, where <span class=math-font>x<sub>1, 2</sub></span> are the roots.</span><br>
+ <p>
+ <strong>Example:</strong><br><br>
+ <span id="m3"></span>
+ </p>
+ <script>
+ const m2 = document.getElementById("m2");
+ const m3 = document.getElementById("m3");
+
+ katex.render(String.raw`(x - x_1)(x - x_2) = 0`, m2, {
+ throwOnError: false
+ });
+ katex.render(String.raw`
+ \begin{aligned}
+ (x - x_1)(x - x_2) &= 0\\
+ (x - (-3))(x - 4) &= 0\\
+ (x + 3))(x - 4) &= 0\\
+ x^2 - 4x + 3x - 12 &= 0\\
+ x^2 - x - 12 &= 0
+ \end{aligned}
+ `, m3, {
+ throwOnError: true
+ });
+ </script>
+ <h2 id="operations">Quadratic Root's Mathematical Operations</h2>
+ <h3 id="operations--formulas">Formulas</h3>
+ <p id="m4"></p>
+ <p id="m5"></p>
+ <h3 id="operations--examples">Examples</h3>
+ <ol>
+ <li>
+ <p>Diketahui persamaan kuadrat <span id="q1"></span>, memiliki akar-akar persamaan kuadrat <span class="math-font">x<sub>1</sub></span> dan <span class="math-font">x<sub>2</sub></span>. Jika <span class="math-font">x<sub>1</sub> < x<sub>2</sub></span>, maka tentukan:
+ <ol type="a">
+ <li><span class="math-font">x<sub>1</sub> + x<sub>2</sub></span></li>
+ <li><span class="math-font">x<sub>1</sub> &times; x<sub>2</sub></span></li>
+ </ol>
+ </p>
+ <hr>
+ <ol type="a">
+ <li><span id="a1"></span></li>
+ <li><span id="a2"></span></li>
+ </ol>
+ </li>
+ </ol>
+ <script>
+ const m4 = document.getElementById("m4");
+ const m5 = document.getElementById("m5");
+ const q1 = document.getElementById("q1");
+ const a1 = document.getElementById("a1");
+ const a2 = document.getElementById("a2");
+
+ katex.render(String.raw`x_1 + x_2 = \dfrac{-b}{a}`, m4, {
+ throwOnError: false
+ });
+ katex.render(String.raw`x_1 \times x_2 = \dfrac{c}{a}`, m5, {
+ throwOnError: false
+ });
+ katex.render(String.raw`2x^2 + 7x + 3 = 0`, q1, {
+ throwOnError: false
+ });
+ katex.render(String.raw`
+ \begin{aligned}
+ x_1 + x_2 &= \dfrac{-b}{a}\\
+ &= \dfrac{-7}{2}\\
+ \end{aligned}
+ `, a1, {
+ throwOnError: true
+ });
+ katex.render(String.raw`
+ \begin{aligned}
+ x_1 \times x_2 &= \dfrac{c}{a}\\
+ &= \dfrac{3}{2}\\
+ \end{aligned}
+ `, a2, {
+ throwOnError: true
+ });
+ </script>
+ <h1>References</h1>
+ <ol>
+ <li id="reference-1" tabindex="-1">Quadratic Equation - The English Wikipedia, <a
+ href="https://en.wikipedia.org/wiki/Quadratic_equation"
+ class="link">https://en.wikipedia.org/wiki/Quadratic_equation</a></li>
+ </li>
+ </section>
+ </div>
+
+ <script src="/scripts/toc.js"></script>
+ <script src="/scripts/sidebar.js"></script>
+</body>
+
+</html> \ No newline at end of file
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