Chapter 2, Problem 6CR

To determine

To label: The vertex and axis of symmetry. Find the minimum and maximum value of the function. Describe where the function is increasing and decreasing.

Answer to Problem 6CR

Vertex is $(1,-4)$ .

The axis of symmetry is $x=1$ .

The parabola opens up and has a minimum value of $y_{\min }=-4$ .

The function is decreasing on the interval $-\infty <x<1$ and decreasing on the interval $1<x<\infty$ .

Explanation of Solution

Given information: $f(x)=3{(x-1)}^2-4$ .

Vertex form of a parabola is $y=a{(x-h)}^2+k$ .

From the given function $f(x)=3{(x-1)}^2-4$ , the vertex $(h,k)$ is $(1,-4)$ .

The vertical line passes through the $x-$ coordinate of the vertex is the axis of symmetry, $x=1$ .

The given function opens up and has a minimum value of $y_{\min }=-4$ .

The graph of the given function is decreasing on the interval $-\infty <x<1$ and decreasing on the interval $1<x<\infty$ .