Question

A ball is thrown straight up from a cliff. The function f(x)= -4.9t^ + 17t +19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is the height reached? Round your answer to one decimal place.

Answer 1

33.7 m at 1.7 seconds

Explanation:

For quadratic ax^2+bx+c, the line of symmetry (x-coordinate of the vertex) is ...

-b/(2a)

For your quadratic, the vertex (highest point) is reached at time ...

t = -(17)/(2(-4.9)) = 17/9.8 ≈ 1.7 . . . . seconds

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The height at that time is ...

f(17/9.8) = (-4.9(17/9.8) +17)(17/9.8) +19 = 289/19.6 +19 ≈ 33.7 . . . meters

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Comment on the function evaluation

We have used the "Horner form" of the function to make evaluation easier.

f(t) = (-4.9t +17)t +19