Question

The quadratic function d = –2x^2 + 15 models a skateboarder’s distance, in feet, from the bottom of a hill x seconds after the skateboarder starts moving down the hill. After how many seconds is the skateboarder 8 ft from the bottom of the hill?

Answer 1

After 1.87 seconds the skateboarder is 8 ft from the bottom of the hill.

Explanation:

The quadratic function d = –2*x² + 15 models a skateboarder’s distance, in feet, from the bottom of a hill x seconds after the skateboarder starts moving down the hill.

You want to know after how many seconds the skater is 8 feet from the bottom of the hill. That is, with the distance being 8 feet, you want to calculate the time t. Replacing in the expression d by the value of 8 feet:

8=–2*x² + 15

Solving:

8-15 = -2*x²

-7= -2*x²

(-7)÷(-2)= x²

3.5= x²

√3.5=x

1.87= x

After 1.87 seconds the skateboarder is 8 ft from the bottom of the hill.