Question

H=-16t^2+27t+3 what is the max height of the soccer ball

Answer 1

h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64

With every number t, h
`\leq` 921/64.

Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)

"=" when 4t = 27/8, or t = 27/32.

Answer 2

To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:

t = -b/2a

where a = -16 and b = 27 from the given equation:

H = -16t^2 + 27t + 3

Substituting these values into the formula, we get:

t = -27/(2(-16)) = 0.84375

Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:

H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625

Therefore, the maximum height of the soccer ball is approximately 12.65625 units.