Ingrid hit a golf ball. The height of the ball (in meters above the ground) \( t \) seconds after being hit is modeled by \( h(t)=-5 t^{2}+30 t \) Ingrid wants to know when the ball reached its highest point. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. \( h(t)=\square \) 2) How many seconds after being hit does the ball reach its highest point?

We start with the function:   h(t) = –5t² + 30t Step 1: Rewrite in vertex form. Factor out –5 from the t² and t terms:   h(t) = –5(t² – 6t) To complete the square for t² – 6t, take half of –6, which is –3, and square it to get 9. Add and subtract 9 inside the parentheses:   h(t) = –5[(t² – 6t + 9) – 9]       = –5[(t – 3)² – 9] Distribute –5:   h(t) = –5(t – 3)² + 45 Thus, the function in vertex form is:   h(t) = –5(t – 3)² + 45 Step 2: Determine when the ball reaches its highest point. In the vertex form, the vertex is given by (3, 45). Since the coefficient of (t – 3)² is negative, the vertex represents the maximum point. Therefore, the ball reaches its highest point at t = 3 seconds.