Question

raven built a rocket for her science project and launched it from a platform to track its path. the hight in feet of the rocket above ground at time t seconds can be modeled by the equation h= -16t^2+32t+4 what is the maximum hight the rocket reaches

Answer 1

Answer:

20ft

Step-by-step explanation:

-16t² + 32t + 4

The main goal to find the maximum height is to find the vertex of the parabola because the vertex is always the minimum or the maximum value.

To find the x value of the vertex, use the formula x = $\frac{-b}{2a}$

The a-value is the first coefficient and the b value is the second coefficient:

x = $\frac{-32}{-32}$

x = 1

We can say x = t because t is the x value in the equation.

Now, we can substitute x back into the original equation to find the y-value for the vertex.

y = -16t² + 32t + 4

y = -16(1)² + 32(1) + 4

y = -16(1) + 32 + 4

y = -16 + 32 + 4

y = 20

In a word problem, height is typically the y-value and time is typically the x-value. Since t = x, the answer is 20.