Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 7 - Polynomial Equations and Factoring - 7.4 - Solving Polynomial Equations in Factored Form - Exercises - Page 382: 42

Answer

$y = (x - 5)(x + 3)$

Work Step by Step

Substituting $y=0$ in the equation, we obtain the $x$-intercepts of the curve. From the graph we notice that there are two $x$-intercepts: one positioned on the right side of the $x$-axis and one on the left side, therefore one $x$-intercept is positive, while the other is negative. Because the positive $x$-intercept is further from the origin that the negative one, it means that the two $x$-intercepts are $$x=-3\text{ and }x=5.$$ Thus the equation is given by $$y=(x-5)(x+3).$$
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