Question

When Darryl jumps into the air, his height in feet above the

surface of the water is given by
h = − 16t² + 5t + 22
-
where t is the amount of time in seconds since he dove.
Use the quadratic formula to help you determine how long it
takes for Darryl to hit the water
t =
seconds

Answer 1

t = 5/32 + sqrt(1433)/32 or t = 5/32 - sqrt(1433)/32

Explanation:

Solve for t over the real numbers:

-16 t^2 + 5 t + 22 = 0

Divide both sides by -16:

t^2 - (5 t)/16 - 11/8 = 0

Add 11/8 to both sides:

t^2 - (5 t)/16 = 11/8

Add 25/1024 to both sides:

t^2 - (5 t)/16 + 25/1024 = 1433/1024

Write the left hand side as a square:

(t - 5/32)^2 = 1433/1024

Take the square root of both sides:

t - 5/32 = sqrt(1433)/32 or t - 5/32 = -sqrt(1433)/32

Add 5/32 to both sides:

t = 5/32 + sqrt(1433)/32 or t - 5/32 = -sqrt(1433)/32

Add 5/32 to both sides:

Answer: t = 5/32 + sqrt(1433)/32 or t = 5/32 - sqrt(1433)/32