Question

Help meeeeeeeeeeeeeeee pleaseee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

help meeeeeeeeeeeeeeee pleaseee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

The maximum value of quadratic function

is at vertex of its parabola.

The maximum value of f(x) = ax² + bx + c is k at x=h

where:
`h=(-b)/(2a)` and k = f(h)

We have t instead of x so it's quadratic function named h with the variable t.

So, the function gets the maximum of k at t=h₁

h(t) = -16x² + 70x + 7 ⇒ a = -16, b = 40

`h_1=(-40)/(2\cdot(-16))=(40)/(32)=\frac54`

It will take 1.25 s for the rocket to reach its maximum height.

`h(h_1)=-16\cdot\left(\frac54\right)^2+40\cdot\left(\frac54\right)+7=-16\cdot(25)/(16)+50+7=-25+57=32`

The maximum height is 32 feet.