Question

2. The path of a high diver is given by y = + (2x2 – 9x – 56), where y is the height of the diver

above the water and x is the horizontal distance from the diving board (in feet). How far from the
end of the diving board is the diver when he hits the water?

Answer 1

The diver will be 8 feet from the end of the board when he hits the water.

Explanation:

The diver hits the water when y = 0.

To find the distance, we have to find the values of x when y = 0.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = (x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

In this problem, we have that:

`y = 2x^(2) - 9x - 56`

`2x^(2) - 9x - 56 = 0`

So

`a = 2, b = -9, c = -56`

Then

`\bigtriangleup = b^(2) - 4ac = (-9)^(2) - 4*2(-56) = 529`

`x_(1) = (-(-9) + √(529))/(2*2) = 8`

`x_(2) = (-(-9) - √(529))/(2*2) = -3.5`

It is a horizontal distance, so the answer is a positive value.

The diver will be 8 feet from the end of the board when he hits the water.