Exercise 72 Page 102

We are asked to describe a real-world situation that involves a quadratic equation. Let's recall that the graph of a quadratic function is a parabola.

Let's look at a couple of examples.

Throwing a Ball

When we throw a football, or any other object, the path it takes through the air can be modeled by a quadratic function.

When we throw the ball, there are some questions that we might ask.

• When does the football reach its maximum height?
• What is its maximum height?

We can answer these question by finding the vertex of the parabola.

The x-coordinate of the vertex tells us when the ball reaches the maximum height, and the y-coordinate tells us the maximum height of the ball.

Parabolic Arches

A parabolic arch is an arch in the shape of parabola. Some of the places that we can see parabolic arches are in huge buildings and on bridges.

• The Gateway Arch monument in St. Louis, Missouri.

• The Golden Gate Bridge.

• Gloucester Cathedral in Gloucester, England.

The vertex of each arch represents the highest or the lowest point in each arch.