When does the ball reach its maximum height?

Question

H = -16t ^2 + 32t + 185

Where H is the height of the ball after t seconds have passed.

Answer 1

For this problem, you would want to find the x-coordinate of the vertex to find when the ball reached its highest point. The equation to find the x-coordinate of the vertex of any given parabola is -b/2a where a is the coefficient of the x^2 term and and b is the coefficient of the x term. Using the formula -b/2a, you would find the vertex of this parabola to be -32/(-16*2) which would be 1. That means the ball reaches its highest point after 1 second.

Bonus: Now that you know the x-coordinate of the vertex and how long it takes for the ball to reach the maximum height, you take this x-coordinate and plug it back into the quadratic formula to find the maximum height (y-coordinate). Plugging 1 into the equation should give you 201. So the maximum height of the ball is 201 (include units if possible)

The ball reaches a maximum height of 201 (include units) after 1 second.

I hope this helps!