Stuck and need help. I don’t know the answer and would appreciate it.

Question

Orange Orthogonals: h(x) = –6x^2 +53x – 91

1. How high is the rocket when it explodes?

2. How many seconds was the rocket in the air before it exploded?

3. How many seconds did the sparkles stay in the air?

4. What method did you use to solve the given equation?

5. Show your work below.

Answer 1

The height can be found from the vertex: The x component of the vertex is equal to -b/2a where the variables a and b are the coefficients of the original equation. b = 53 and a = -6. thus x = -53/2(-6) or 53/12. This value is put back in to find the height. -6(53/12)^2 + 53 (53/12) -91.

-19.507 + 234.083 - 91 = 123.58 as the height.

If x is in seconds then the rocket was in air before explosion for 53/12 seconds or 4 5/12 seconds or at the vertex.

The sparkles took as much time to go down as the rocket took to go up: 4 5/12 seconds.