How do i solve this problem while creating a quadratic equation ?

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

correct answers below: