Chapter 8.3, Problem 2Q

To determine

To identify: The properties of the parabola from the graph.

Explanation of Solution

Given information:

The graph is shown in Figure 1.

  

Figure 1

The general form of the quadratic equation is $y=a{x}^2+bx+c$ whose graph is always parabola.

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 the parabola is opens upward.

It can be seen from the graph that it is form of the parabola whose vertex is $\left(-2,5\right)$ 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 $\left(-2,5\right)$ .

Therefore, the symmetrical axis is $x=-2$ .

The domain of the parabola is the set of real numbers since the function is smooth and continuous.

The range is the set of output value of the function.

It can be seen from the graph that the range of the parabola is $\left[5,-\infty \right]$ .