## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 3 - 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 249: 61

#### Answer

One that opens upwards: $y=x^2+\frac{7}{2}x+\frac{3}{2}$ One that opens downwards: $y=-x^2-\frac{7}{2}x-\frac{3}{2}$

#### Work Step by Step

Use: $y=a(x-x_1)(x-x_2)$, where $x_1$ and $x_2$ are the $x$ of the x-intercepts. $y=a[x-(-3)][x-(-\frac{1}{2})]=a(x^2+\frac{1}{2}x+3x+\frac{3}{2})=a(x^2+\frac{7}{2}x+\frac{3}{2})$ One that opens upwards ($a\gt0$). $y=1(x^2+\frac{7}{2}x+\frac{3}{2})=x^2+\frac{7}{2}x+\frac{3}{2}$ One that opens downwards ($a\lt0$). $y=-1(x^2+\frac{7}{2}x+\frac{3}{2})=-x^2-\frac{7}{2}x-\frac{3}{2}$

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