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?

To convert the quadratic function \( h(t) = -5t^2 + 30t \) into vertex form, we can complete the square. First, factor out -5 from the first two terms: \( h(t) = -5(t^2 - 6t) \). Then, complete the square: \( h(t) = -5(t^2 - 6t + 9 - 9) = -5((t - 3)^2 - 9) = -5(t - 3)^2 + 45 \). Thus, \( h(t) = -5(t - 3)^2 + 45 \). The ball reaches its highest point at \( t = 3 \) seconds after being hit. In this vertex form, the highest point is represented as the vertex of the parabola, which is located at \( (3, 45) \) — 3 seconds and 45 meters high!