Chapter 2.2, Problem 22E

To determine

To find: To graph the function, label the vertex and axis of symmetry.

Answer to Problem 22E

The vertex of the function $y=3x^2-6x+4$ is $(1,1)$ .

Axis of symmetry $x=1$ .

  

Explanation of Solution

Given information: $y=3x^2-6x+4$ .

Identifying the vertex:

General form of a quadratic function $y=a{x}^2+bx+c$ ,

From the function $y=3x^2-6x+4$ ,

  $a=3,b=-6,c=4$

The $x-\text{coordinate}$ of a quadratic function is $x=-\frac{b}{2a}$ ,

  $\begin{array}{l}x=-\frac{(-6)}{2\times 3}\\ x=-\frac{(-6)}{6}\\ x=1\end{array}$

Substituting $x=1\text{in}y=3x^2-6x+4$ ,

  $\begin{array}{l}$ y=3{(1)}^2-6(1)+4$y=3-6+4\\ y=1\end{array}$

The vertex of the given quadratic function $(h,k)$ is $(1,1)$ .

The axis of symmetry is a vertical line which passes through the vertex of the parabola.

The $x-\text{coordinate}$ of the vertex is the equation of axis of symmetry $x=1$ .