Chapter 8.4, Problem 19E

To determine

To find the vertex and the axis of symmetry of the graph of the given function $f(x)=3{\left(x+1\right)}^2$

Answer to Problem 19E

The vertex $(-1,0)$ and the axis of symmetry $x=-1$ .

Explanation of Solution

Given information :

Given function $f(x)=3{\left(x+1\right)}^2$

The vertex of the graph of $f(x)=k{(x-h)}^2\left(\text{where}\text{k}\text{is}\text{constant}\right)$ is $(h,0)$ and the axis of symmetry is $x=h$ .

Now compare given function $f(x)=3{\left(x+1\right)}^2$ with $f(x)={(x-h)}^2$ , we get $h=-1$

Hence, the vertex $(-1,0)$ and the axis of symmetry $x=-1$ .