Question

Rebekah kicks a soccer ball off the ground and in the air with an initial velocity of 25 feet per second. Using the formula H(t) = -16t^2 + vt + s, what is the maximum height the soccer ball reaches?

9.5 feet

9.8 feet

10.2 feet

10.7 feet

Answer 1

@zepdrix

Answer 2

if Rebekah is kicking the ball off the ground
what do you think would be the "initial height" the ball is moving from?

Answer 3

0 right, because it starts from the ground

Answer 4

\(\bf \text{initial velocity}\\
h = -16t^2+v_ot+h_o \qquad \text{in feet}\\
\\ \quad \\

v_o=\textit{initial velocity of the object}\to 25\\
h_o=\textit{initial height of the object}\to 0\\
h=\textit{height of the object at "t" seconds}
\\ \quad \\ \quad \\
h(t) = -16t^2 + vt + s\implies h(t) = -16t^2 + 25t + 0\)

notice the equation is a parabola, and it has a negative leading term coefficient, -16
meaning the parabola opens DOWNwards


so what you're really asked is
what's the y-coordinate of the vertex of that equation or parabola ?