Chapter 9.2, Problem 26P

Open-Ended For Exercises 24-26, given an example of a quadratic function with the given characteristic (s).

Its vertex lies on the $x$-axis and the graph opens down.

To determine

To find the quadratic function.

Answer to Problem 26P

The required quadratic function is $f\left(x\right)=-x^2.$

Explanation of Solution

Given information: Given parent function $y=x^2.$

Calculation:

Use the parent function $y=x^2.$

Which has its vertex at $\left(0,0\right)$ and opens up.

The parabola opens down so $a<0.$ in this case.

So, retain its coefficient: $a=-1$ for simplicity.

Since the vertex already lies on the x-axis so do not need any vertical shift;

Thus, the required quadratic function is $f\left(x\right)=-x^2.$