Chapter 9.2, Problem 24P

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

Its graph opens up and has its vertex at $(0,-3).$

To determine

To find the quadratic function.

Answer to Problem 24P

The required quadratic functionis $f\left(x\right)=x^2-3.$

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 parent function already opens upward.

So, retain its coefficient: $a=1.$ note that use $a>0$ in this case.

Since the vertex at $\left(0,-3\right)$ , translate the parent function $3$ units down:

Thus, the required quadratic functionis $f\left(x\right)=x^2-3.$