An event in the Summer Olympics is 10-meter springboard diving. In this event, the height s, in meters, of a diver above the water t seconds after jumping is given by s(t) = –4.9t2 + 7.1t + 10. What is the maximum height that the diver will be above the water? Round to the nearest tenth

M= __________

Since you labeled it "college" algebra, I will assume you know Calculus

s(t) = -4.9t^2 + 7.1t + 10
v(t) = -9.8t + 7.1
= 0 for a max of s(t)

9.8t = 7.1
t = 71/98

s(71/98) = -4.9*71/98)^2 + 7.1(71/98) + 10
= appr 12.58 m

or 12.6 m above water (to the nearest tenth)

To find the maximum height that the diver will be above the water, we need to determine the vertex of the parabolic function s(t) = -4.9t^2 + 7.1t + 10. The vertex of a parabola is the point at which it reaches its maximum or minimum value.

The formula to find the vertex of a quadratic function in the form of f(x) = ax^2 + bx + c is given by:
x = -b / (2a)

In this case, the function is s(t) = -4.9t^2 + 7.1t + 10, where a = -4.9 and b = 7.1. Plugging these values into the formula, we get:
t = -7.1 / (2 * -4.9)

Now we can find the maximum height by substituting this value t back into the function s(t). Therefore:
s(max height) = -4.9 * (-7.1 / (2 * -4.9))^2 + 7.1 * (-7.1 / (2 * -4.9)) + 10

Simplifying this expression will give us the maximum height above the water.

M = __________ (Round to the nearest tenth)