Chapter 8.3, Problem 6E

To determine

To find: The vertex, the axis of the symmetry and the $y$ -intercept of the graph.

Answer to Problem 6E

The vertex is $\left(-1,1\right)$ , the axis of the symmetry is $x=-1$ and the $y$ -intercept of the graph is $\left(0,5\right)$ .

Explanation of Solution

Given information:

The graph is shown in Figure 1.

  

Figure 1

The behavior of the graph of the parabola is U shaped curve where axis of symmetry can be drawn through the vertex of parabola.

It can be seen from the graph that it is form of the parabola whose vertex is $\left(-1,1\right)$ since the parabola is symmetrical through the vertex.

It can be seen from the graph that the axis of symmetry is the vertical line.

The vertical symmetry passes through the vertex $\left(-1,1\right)$ .

Therefore, the symmetrical axis is $x=-1$ .

The y -intercept is the point where the value of $x=0$ or the point where the function intersects the y -axis.

It can be seen from the given graph parabola intersect the y-axis at point $\left(0,5\right)$ .

Therefore, the y -intercept is $\left(0,5\right)$ .