Question

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

Answer 1

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