Chapter 8.6, Problem 12E

To determine

To plot: The points on the graph and identify the representation of the points.

Answer to Problem 12E

Thepoints represents the quadratic equation.

Explanation of Solution

Given information:

The points are $\left(-1,3\right),\left(-3,5\right),\left(0,-1\right),\left(1,5\right),\left(2,15\right)$ .

Plot the points on the graph as shown in Figure 1.

  

Figure 1

The behavior of the graph of the parabola is U shaped curve that is open upward or downward where the axis of symmetry can be drawn through the vertex of parabola at which the parabola is symmetric whose equation is the quadratic equation.

The parabola decreases until the vertex then starts increasing or the parabola increases until the vertex then starts decreasing

It can be seen from the points of the graph that it is form of the parabola whose vertex is $\left(-1,-3\right)$ since the parabola is symmetrical through the vertex and the parabola decreases till vertex then starts increasing.

Therefore, the points on the graph represents the parabola with vertical symmetry $x=-1$ that means points represent a quadratic equation.