Question

Suraj watched a hovercraft take off from a platform. The height of the hovercraft (in meters above the ground) ttt minutes after takeoff is modeled by h(t)=-4t^2+8t+32h(t)=−4t 2 +8t+32h, left parenthesis, t, right parenthesis, equals, minus, 4, t, squared, plus, 8, t, plus, 32 Suraj wants to know when the hovercraft will reach its highest point.

Answer 1

The hovercraft will reach its highest point 1 minute after takeoff.

Step-by-step explanation:

To find the highest point of the hovercraft's trajectory, we need to determine the vertex of the quadratic function h(t) = -4t^2 + 8t + 32. The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)). In this case, a = -4 and b = 8, so the vertex is at (-8/(2*-4), h(-8/(2*-4))). Simplifying, we find that the vertex is at (1, 36). Therefore, the hovercraft will reach its highest point after 1 minute since takeoff.

Answer 2

1) The vertex form of the function reveals when the hovercraft reached its highest point:

h(t)=-4\left(t-1\right)^2+36h(t)=−4(t−1)

2

+36h, left parenthesis, t, right parenthesis, equals, minus, 4, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 36

2) The hovercraft reached its highest point 111 minute after takeoff.