Jasmine is diving off a 3-meter springboard. her height in meters above the water when she is x meters horizontally from the end of the board is approximated by the equation h=-x^2+3x+3. what is the maximum height jasmine will reach on her dive?

5.25 m

Explanation:

Given;

The height equation h;

h=-x^2+3x+3

Where;

h = the height above water

x = horizontal distance from the end of the board

The maximum height is at h' = 0, when change in h with respect to change in x is equal to zero.

differentiating the equation h.

dh/dx = h' = - 2x + 3 = 0

Solving for x;

2x = 3

x = 3/2

Substituting into the function h;

h max = - x^2+3x+3

h max = - (3/2) ^2 + 3 (3/2) + 3 = - 9/4 + 9/2 + 3 = 9/4 + 3 =

h max = 21/4 = 5.25 m