What is the coordinate of the vertex of the function and explain the interpretation of the vertex in this context?

Question

devyn and erin are both members of the same springboard diving team. Devyn competes on the 3-meter springboard. Devyn would like to generate on initial velocity of 10 meterper second, which would be approximated by the function h(t)=-5t^2+10+3 where t represents time in seconds and h(t) represents height in meters.

Answer 1

I will assume there is a typo in the height equation and it is actually h(t) = -5t² +10t +3. For a given quadratic y = ax² + bx + c, the vertex (h, k) is found by computing h = ^–b/_2a, and then evaluating y at h to find k.

For this equation, h = -10/[2(-5)] = 1. Solving for k, k = h(1) = -5(1)²+10(1)+3 = 8

So the vertex is located at (1,8), which is the highest point of the concave down parabola describing the trajectory of the diver. Concave down because of the minus sign preceding the 5 in the equation.