How do I factor the relation: h= -0.3d^2 +1.2d +1.5 to determine the distance between his take-off and landing

Question

Derick who is mountain biking jumps off a ledge. His path is modelled by the quadratic relation: h= -0.3d^2 +1.2d +1.5, where h is the height above the ground and d is the horizontal distance between his take-off and landing.

Answer 1

distance = 5 -(-1) = 6 between lift off and landing

h = -.3d^2 +1.2d +1.5 = 0 at left off & landing

divide by-.3 to get

d^2 -4d -5 = 0

factor

(d -5)(d+1) = 0

set each factor = 0 and solve for d

d =5 and -1

subtract

-1 from 5 = 6

Answer 2

Hello Veronica,

The relation you mentioned is: h = -0.3d² +1.2d +1.5

You could factor out -0.3, the coefficient of d² . You would get: h = -0.3 (d² -4d -5) because -0.3*(-4) = -1.2 and -0.3*(-5) = 1.5

Now see how to factor d² -4d -5: two integers whose sum is -4 and whose product is -5? That'd be -5 and 1

So you can factor d² -4d -5 as (d-5)(d+1). If you're keeping track, you can now write the original relation as

h = -0.3 *(d-5)(d+1)

To determine the distance between take-off and landing, keep in mind that at landing, the height h is equal to ZERO. So set -0.3 *(d-5)(d+1) = 0, solve for d. You have d-5 = 0 OR d+1=0.

That means: d = 5 OR d = -1

d is the distance between take-off and landing. ONLY one of those answers makes sense. I'll let you figure that out (hint: distance can't be negative).

Cheers.