Question

At what time does the donut reach its maximum height? second The following equation represents the path of a donut hole being thrown by Ms. Doll where x represents the time the donut is in the air and y represents the height of the donut. y=-x²+4x-2

Answer 1

The donut reaches its maximum height of 2 units at 2 seconds.

Step-by-step explanation:

The maximum height of the donut can be found by determining when the vertical velocity, represented by Vy, switches from positive (upwards) to negative (downwards). This occurs when Vy = 0. In the given equation y = -x² + 4x - 2, we can find the time when Vy = 0 by setting the derivative of y with respect to x equal to 0.

By solving for x in the equation 0 = -2x + 4, we find that x = 2. Substituting x = 2 into the equation y = -x² + 4x - 2, we can find the maximum height by evaluating y.

Now, substitute x = 2 into the equation y = -x² + 4x - 2 and solve for y.
y = -(2)² + 4(2) - 2
y = -4 + 8 - 2
y = 2

Therefore, the donut reaches its maximum height of 2 units at 2 seconds.