Chapter 8.3, Problem 5E

To determine

Tofind:The vertex, axis of symmetry and y- intercept of the graph.

Answer to Problem 5E

The vertex of the graph is at point $\left(2,-1\right)$ , equation of axis of symmetry is $x=2$ , and the y-intercept of the graph is $\left(0,1\right)$ .

Explanation of Solution

Given information:

The graph is shown in Figure-1 here.

Formulaused:

The vertex of the graph is point where minimum or maximum of the graph exists. The axis of symmetry of the graph divides the graph into two identical parts. The y-intercept is a point where graph meet y-axis.

Calculations:

The labelled graph from the given graph is shown in Figure-2.

  

The given graph opens-up and its minimum exists at point $\left(2,-1\right)$ , hence the vertex of the graph is at point $\left(2,-1\right)$ .

The line $x=2$ divides the graph into two identical parts, so $x=2$ is the equation of axis of symmetry.

The graph intersect y −axis at point $\left(0,1\right)$ , hence y-intercept of the graph is $\left(0,1\right)$ .

Conclusion:

The vertex of the graph is at point $\left(2,-1\right)$ , equation of axis of symmetry is $x=2$ , and the y-intercept of the graph is $\left(0,1\right)$ .