Chapter 9.3, Problem 38HP

To determine

Write a quadratic function that opens downward and is wider than parent graph.

Answer to Problem 38HP

  $f(x)=-\frac{1}{4}{x}^2$ is an example of a quadratic function that opens downward and wider than the parent graph.

Explanation of Solution

Given:

Write a quadratic function that opens downward and is wider than parent graph.

Concept Used:

If the parent graph is $f(x)=a{x}^2$ , then it opens upward. In order to open downward, the value of $a$ must be negative.

So $f(x)=-x^2$ is a quadratic function that opens downward.

In order to be wider than the parent graph, the value of $\left|a\right|$ must be between 0 and 1.

Therefore, if $a=-\frac{1}{4}$ , the graph will be wider.

So, $f(x)=-\frac{1}{4}{x}^2$ is an example of a quadratic function that opens downward and wider than the parent graph.

Thus, $f(x)=-\frac{1}{4}{x}^2$ is an example of a quadratic function that opens downward and wider than the parent graph.