Question

A water balloon is tossed upwards from the edge of building. The height of the balloon is given by the equation h(t) = -5t² + 20t + 25 where h is in meters and time t is in seconds.

Find the vertex from the equation for h.

Answer 1

To find the vertex of the quadratic equation h(t) = -5t² + 20t + 25, we calculate the time component as -b/(2a) which is 2 seconds, and then plug this back into the equation to get the maximum height, which is 45 meters. Hence, the vertex is at (2, 45).

Step-by-step explanation:

To find the vertex of the parabola represented by the quadratic equation h(t) = -5t² + 20t + 25, where h is in meters and t is in seconds, we will use the vertex formula for parabolas of the form y = ax² + bx + c.

The vertex formula gives the x-coordinate as -b/(2a). For our equation, a = -5 and b = 20, so the x-coordinate of the vertex, which corresponds to the time t, is -20/(2 · -5) = 2 seconds. To find the y-coordinate of the vertex, which represents the maximum height, we substitute t = 2 into the original equation h(t) to get h(2) = -5(2)² + 20(2) + 25 = -5 · 4 + 40 + 25 = 45 meters. Therefore, the vertex of the parabola is at (2, 45).