Find the maximum height of the rocket and explain in at least threes sentence how you calculated your answer of y = - 16x ^ 2 + 480x

The maximum height of the rocket is 3600

Step-by-step explanation:

The vertex of the quadratic equation y = ax² + bx + c is (h, k), where

The height of the rocket calculated using the equation y = -16x² + 480x, where y is the height and x is the time

To find the maximum height, do that

Let us do that

∵ y = -16x² + 480x

∴ a = -16 ⇒ the vertex is a maximum point

∴ b = 480

→ Use the rule above to find h

∵ h =

∴ h = =

∴ h = 15

∵ k = y at x = h

→ Substitute x by 15 in the equatuion and y by k to find x

∵ k = -16(15)² + 480(15)

∴ k = -3600 + 7200

∴ k = 3600

∵ The maximum height equal the value of k

∴ The maximum height of the rocket is 3600

c is the final answer! : )

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.