Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 55


$\left(-3,13 \right)$ and $\left(5,21\right)$

Work Step by Step

To find the points of intersection of $f(x)$ and $g(x)$, solve $f(x)=g(x)$: \begin{align*} x^2-x+1&=2x^2-3x-14\\ 0&=-x^2+x-1+2x^2-3x-14\\ 0&=x^2-2x-15 \end{align*} By Factoring: $$0=(x+3)(x-5)$$ Use the Zero-Product Property by equating each factor t zero, then solve each equation to obtain: \begin{align*} x+3 &=0 &\text{ or }& &x-5=0\\ x&=-3 &\text{ or }& &x=5\\ \end{align*} To find the $y$-coordinates of the points of intersection, evaluate either of the two functions at $x=-3$ and $x=5$ to obtain: $f(-3)=(-3)^2-(-3)+1=13$ $f(5)=(5)^2-(5)+1=21$ Therefore, the points of intersection are: $\left(-3,13 \right)$ and $\left(5,21\right)$
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