Help me please it’s due today

49 ft  

Step-by-step explanation:

h(t) = 56t - 16t²

This is the equation of a parabola.

We must solve the equation to find the time (t) when the ball reaches its maximum height (h).  

The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.

One way to solve this problem is to convert the equation to the vertex form.

We do that by completing the square.

Calculation:

h = -16t² + 56t  

Divide both sides by -16 to make the coefficient of  t² equal to 1.

(-1/16)h = t² - ⁷/₂t

Square half the coefficient of t

(-7/4)² = 49/16

Add and subtract it on the right-hand side

(-1/16)h = t² - ⁷/₂t  + 49/16 - 49/16  

Write the first three terms as the square of a binomial

(-1/16)h = (t - ⁷/₄)² - 49/16

Multiply both sides by -16

h = -16(t - ⁷/₄)² + 49

You have converted your equation to  the vertex form of a parabola:

y = a(t - h)² + k = 0,

where (h, k) is the vertex.

h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).

The time to reach maximum height is ⁷/₄ s = 1.75 s.

The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.