Question

A baseball is thrown up in the air. The table shows the heights y (in feet) of the baseball after x seconds. Write an

equation for the path of the baseball and use the equation to predict the height of the ball at time 5 seconds.

Answer 1

The equation for the path of the baseball is y = -2x² + 12x + 6; height at 5 seconds = 16 ft

How to determine the equation for the path of the baseball

From the question, we have the following parameters that can be used in our computation:

The table of values

A quadratic function is represented as

y = ax² + bx + c

Where,

c = y when x = 0

So, we have

y = ax² + bx + 6

Using the table values, we have

4a + 2b + 6 = 22

16a + 4b + 6 = 22

So, we have

4a + 2b = 16

16a + 4b = 16

This gives

8a + 4b = 32

16a + 4b = 16

Evaluate

8a = -16

a = -2

Next, we have

4a + 2b = 16

4(-2) + 2b = 16

2b = 16 + 8

2b = 24

b = 12

So, we have

y = -2x² + 12x + 6

At time 5 seconds, we have

y = -2 * 5² + 12 * 5 + 6

y = 16

Hence, the equation for the path of the baseball is y = -2x² + 12x + 6