Question

Ingrid hit a golf ball. The height of the ball (in meters above the ground) t seconds after being hit is modeled by h(t)= -5t^2+30t

Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=
How many seconds after being hit does the ball reach its highest point? seconds

Answer 1

The function h(t) = -5t^2 + 30t can be rewritten in vertex form as h(t) = -5(t - 3)^2 + 45.

Step-by-step explanation:

The given function h(t) = -5t^2 + 30t represents the height of the golf ball in meters above the ground at time t seconds after being hit. To find the vertex form of the function, we can complete the square.

First, let's rewrite the function by factoring out a -5 from the polynomial: h(t) = -5(t^2 - 6t).

To complete the square, we need to add and subtract the square of half of the coefficient of t, which is 6/2 = 3. So, the function can be rewritten as: h(t) = -5(t^2 - 6t + 9 - 9).

Now, let's factor the perfect square trinomial: h(t) = -5((t - 3)^2 - 9).

Finally, we can simplify the equation: h(t) = -5(t - 3)^2 + 45.