Paige launched a ball using a catapult she built. The height of the ball (in meters above the ground)
\[t\] seconds after launch is modeled by
\[h(t)=-5t^2+40t\]
Paige wants to know when the ball will hit the ground.
1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation.
\[h(t)=\]
2) How many seconds after launch does the ball hit the ground?
seconds

21 of 30

To determine when the ball will hit the ground, we need to find the time \( t \) when the height \( h(t) \) is zero.

### 1. Rewrite the Function in a Different Form

The given function is:
\[ h(t) = -5t^2 + 40t \]

We can factor this quadratic equation to make it easier to find the roots (i.e., when \( h(t) = 0 \)).

First, factor out the greatest common factor (GCF):
\[ h(t) = -5t(t - 8) \]

Now we have the factored form:
\[ h(t) = -5t(t - 8) \]

### 2. Find When the Ball Hits the Ground

To find when the ball hits the ground, set \( h(t) = 0 \) and solve for \( t \):
\[ -5t(t - 8) = 0 \]

This equation is satisfied

Learn how to find when a ball hits the ground using the quadratic equation h(t) = -5t^2 + 40t. This problem involves solving quadratic equations and understanding projectile motion in physics. Suitable for students in Grades 7-9.

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