Question

Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.

1. At what time will Lindsey be 30 feet in the air?

2. How high is the diving board? Explain your thinking.

Answer 1

1.
`x = 2.45s`

2. The diving board is 45 ft high.

Explanation:

• When Lindsey is 30 feet in the air, y = 30.

`30 = -16x^2 + 33x +45\\\\-16x^2 + 33x +15 = 0\\\\16x^2 - 33x -15 = 0\\`

Using quadratic formula, solve for x:

`x = \frac{33 + \sqrt[]{(-33)^2 - 4(16)(-15)} }{2(16)}`

`x = 2.45s`

• If we calculate the height of Lindsey in the air when she is standing on the diving board, we can find the height of the diving board above the ground.

When she is standing on the board, x = 0 as no time has passed after jumping.

`y = -16(0)^2 + 33(0) +45\\\\y = 45 ft`