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 2.4 Properties of Quadratic Functions - 2.4 Assess Your Understanding - Page 157: 17


$\bf{Option \ (H)}$

Work Step by Step

1) The graph of the quadratic function $f(x) = ax^2+bx+c$ is a parabola that opens: (a) Upward when $a \gt 0$ and its vertex has a minimum value. (b) Downward when $a \lt 0$ and its vertex has a maximum value. On comparing $f(x)=x^2-2x$ with $f(x) = ax^2+bx+c$, we get: $a=1, b=-2,c=0; a \gt 0$. We can see that the given function shows a graph of a parabola that opens upward. 2) The coordinates of the vertex of a quadratic function $f(x) = ax^2+bx+c$ are given by: $\displaystyle(\frac{-b}{2a}, f(-\frac{2}{a}))$ Therefore, the coordinates of the function's vertex can be expressed as: $\displaystyle(\frac{-(-2)}{2(1)}, f(-\frac{-2}{2(1)})) $ The minimum value is: $f(1)=(1)^2-(2)(1)=-1$ Thus, the parabola that opens upward and whose vertex is at $(1,-1)$ matches with $\bf{Option \ (H)}$.
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