Chapter 9.3, Problem 20PPS

To determine

Match the graph according to the equation.

Answer to Problem 20PPS

The correct choice is B.

Explanation of Solution

Given:

The function: $y=\frac{1}{3}{x}^2+4$

Concept Used:

The function can be written $f(x)=a{x}^2+c,$ , where $a=\frac{1}{3}\text{and}c=+4$ .

If c is positive, then the graph translated up and if c is negative, then the graph translated down.

Since $0<a<1$ and c is negative, the graph of $y=\frac{1}{3}{x}^2+4$ is the graph of $y=x^2$ vertically compressed by a factor $\frac{1}{3}$ and shifted up 4 units.

So, the correct choice is B.

Thus, the correct choice is B.