Answer:
f(x) = -15x² + 50x
Step-by-step explanation:
You're given the rocket start at ground level, so we can assume,
f(0) = 0
after 1 second the rocket is 35 feet up.
f(1) = 35
and after 2 second the rocket is 40 ft up.
f(2) = 40
Now you have 2 values to plug in your formula to solve.
Plug in f(x) = ax² + bx + c and solve:
f(0) = a(0)² + b(0) + c = 0
f(1) = a(1)² + b(1) + c = 35
f(2) = a(2)² + b(2) + c = 40
a(0)² + b(0) + c = 0
a(1)² + b(1) + c = 35
a(2)² + b(2) + c = 40
0 + 0 + c = 0 , we got c=0, so substitute it
a + b + c = 35
4a + 2b + c = 40
Solve for a and b
c = 0
a + b + 0 = 35
4a + 2b + 0 = 40 , solve it using elimination
-2a - 2b + 0 = -70
4a + 2b + 0 = 40
2a + 0 = -30
a = -15 , we got a, solve for b now
a + b + 0 = 35
(-15) + b + 0 = 35
b = 50
Now we got c=0, a=-15, and b=50, plug it back in your equation
f(x) = -15x² + 50x + 0
