<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-graphing-quadratics-by-factoring">Graphing Quadratics by Factoring Exercise</a></span></p><p>To graph a quadratic equation, all you really need is the vertex (the minimum or maximum point) and the $x$-intercepts (if the quadratic has any). Thus, <span style="color:#27ae60;">Graphing Quadratics by Factoring</span> is actually quite straightforward if the quadratic equation is factorable.</p>
<p><strong><span style="color:#8e44ad;">How do we do it?</span></strong></p>
<p><strong>Step 1</strong>: If the quadratic equation is factorable, factor it. You can see an example below:</p>
<p>$$y = x^2 + 8x + 15$$</p>
<p>$$y = (x+3)(x+5)$$</p>
<p><strong>Step 2</strong>: Set $y$ equal to $0$ to find the two $x$-intercepts.</p>
<p>$$0 = (x+3)(x+5)$$</p>
<p>$$x = -3, -5$$</p>
<p><strong>Step 3</strong>: Find the vertex (the minimum $y$-value) by plugging in the $x$-value that is precisely between the two $x$-intercepts. In this case, our two $x$-intercepts are $-3$ and $-5$. The $x$-value right in the middle is $x = -4$. Plug it in to the original quadratic to get the minimum $y$-value (see below):</p>
<p>$$y = (-4)^2 + 8(-4) + 15$$</p>
<p>$$y = -1$$</p>
<p><strong>Step 4</strong>: Graph the parabola. It's actually quite easy now that we have three points, the two $x$-intercepts and the vertex.</p>
<p style="text-align: center;"><strong>$x$-intercept$_1$</strong>: $(-3, 0)$</p>
<p style="text-align: center;"><strong>$x$-intercept$_2$</strong>: $(-5, 0)$</p>
<p style="text-align: center;"><strong>vertex (minimum value)</strong>: $(-4, -1)$</p>