A cliff diver's height above the water, in meters, is modeled by the function h (d) = - d^2+2d+24, where d represents how far the diver is from the cliff. How far from the cliff will the diver be when she reaches the water

H (d) = height from water

when he reaches the water, his height from water=0

so set the equation equal to zero and solve

0=-d^2+2d+24

multiply both sides by - 1 for ease

0=d^2-2d-24

now find what 2 factors of - 24 add up to - 2

answer is - 6 and 4

0 = (d-6) (d+4)

set each to zero

d-6=0

d=6

d+4=0

d=-4

you cannot have negative distance because that means he hasn't jumped yet so get rid of this number

d=6

answer is 6 meters