College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises: 2

Answer

(a) $h$, $k$ (b) $\text{upward}; \text{minimum}$ (c) $\text{downward}; \text{maximum}$

Work Step by Step

RECALL: (1) Th graph of a quadratic function is a parabola. (2) The standard form of a quadratic function is $f(x) = a(x-h)^2+k$ where $(h, k)$ is the vertex. The graph opens upward when $a \gt 0$ and opens downward when $a \lt 0$. (3) The quadratic function $f(x) = (x-h)^2+k$ has $k$ as its (i) minimum when $a\gt0$; and (ii) maximum when $a \lt 0$ Thus, the missing expression in the given statements are: (a) $h$, $k$ (b) $\text{upward}; \text{minimum}$ (c) $\text{downward}; \text{maximum}$
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