Chapter 9.1, Problem 72HP

To determine

To describea real-world situation which involves a quadratic equation.

Answer to Problem 72HP

The height of a soccer ball that is kicked in the air can be represented by a quadratic equation. The vertex would signify the highest point reached by the ball.

Explanation of Solution

Given information :

Quadratic equation in real life situation.

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.

The axis of symmetry bisects the parabola into two equal parts. Hence each point on the parabola would have an equal point on the other side of the axis of symmetry

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.

If a soccer ball is kicked in the air it would reach a certain height and then eventually drop to the ground. The phenomenon can be represented by a downward facing parabola defined by a quadratic equation.

As mentioned above, for a downward facing parabola $a<0$ . It has a highest point called the maximum which is the vertex. In the situation considered here, the vertex would signify the highest point reached by the soccer ball when kicked in the air.