Given the quadratic function f (a) = d^2 - 7d + 6

Question

Factor the equation into a binomial product.
Solve for the roots of the equation.
This quadratic function models the path, height in feet as a function of distance in
feet, that a diver takes when they dive from a platform at the edge of a pool. How far
away will the diver be from the edge of the pool when they return to the surface?

Answer 1

h = d^2 - 7d + 6 = (d-1)(d-6)
so the diver hits the water 1 ft away, and surfaces 6 ft away.
Those are the roots of the equation -- when height=0

Answer 2

(d-1)(d-6)=0
d-1=0 or d-6=0
d=1 or d=6

Therefore, the diver will be 6 ft away from the edge of the pool when they return to the surface.