Two rockets were launched from a rooftop. The heights of the rockets x seconds after being launched are modeled by the functions shown below. (Shown in additional info). Which statement is true?

Question

ROCKET F: f(x)=-4x^2+29x+24

ROCKET G: g(x)=-5x^2+26x+24

 

A. Rocket F hit the ground 2 seconds after Rocket G

B. Rocket F hit the ground 2 seconds before Rocket G

C. Rocket F hit the ground 3 seconds after Rocket G

D. Rocket F hit the ground 3 seconds before Rocket G

Answer 1

We can compare the times the rockets each hit the ground by setting f(x)=0 and g(x)=0 and solving for each x.

-4x²+29x+24=0 (for F) and -5x²+26x+24=0 (for G).

We can negate each quadratic:

4x²-29x-24=0=(4x+3)(x-8),  so it takes 8 seconds for F to hit the ground; 5x²-26x-24=0=(5x+4)(x-6), so it takes 6 seconds for G to hit the ground. G hits the ground 2 seconds before F, that is, F hits the ground 2 seconds after G, answer A.