Chapter 9.2, Problem 37PPS

To determine

To describe and graph the contrast in the given pair of functions,

Explanation of Solution

Given information :

Given functions are $y=3x^2$ and $y=-3x^2$ .

Graph :

  

Interpretation :

The graph of a quadratic equation ( $y=a{x}^2+bx+c$ ) is a parabola. The parabola is symmetric in nature and the point of symmetry is known as the vertex. This vertex lies on the line of symmetry and is symmetric about this line.

This vertex point shall be:

Highest point (if $a<0$ ) and be called the maximum. Here, the graph opens downwards.

Or, lowest point (if $a>0$ ) and can be called the minimum. Here the graph opens upwards.

In this case, ‘a’ is lesser than 0 hence the graph will have a maximum and will open downwards.

A parabola always points to infinity, either negative or positive.

In the function $y=-3x^2$ , the value of a is negative and thus it opens downwards. Therefore, the contrast of the function with respect to the graph of $y=3x^2$ , as seen in the graph shown above, is that the function has been inverted and now it open downwards.