Algebra 1

Published by Prentice Hall

Chapter 9 - Quadratic Functions and Equations - 9-1 Quadratic Graphs and Their Properties - Practice and Problem-Solving Exercises - Page 538: 30

Answer

Domain: $-\infty < x < \infty$ Range: $-\infty < y \leq -1$

Work Step by Step

The equation given is: $f(x) = -2x^2-1$ First, we find the domain. All polynomials are continuous from $(-\infty,\infty)$, so the domain is $-\infty < x < \infty$. Now, we find the range. This quadratic's equation is $f(x) = ax^2+c$. Since $a$ is negative, the graph is facing downwards, like this: $\bigcap$ Therefore, there is a maximum. Since there is no horizontal translation, since $b = 0$, the maximum y-value -s $f(0) = -1$. Thus, the range is from $(-\infty, -1]$. Or, in another form, $-\infty < y \leq -1$

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