SOLUTION: A tennis ball is rolled down a valley along a slope shaped like a parabola. After t seconds, its height above sea level in meters is modeled by the function h(t) = t2

Question 366048: A tennis ball is rolled down a valley along a slope shaped like a parabola. After t seconds, its height above sea level in meters is modeled by the function h(t) = t2 – 10.2t + 18. After how many seconds does the ball reach its minimum height? What is that minimum height? Round your answers to the nearest hundredth’s place; use proper units in your answer.
Answer by nerdybill(7003) (Show Source):
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A tennis ball is rolled down a valley along a slope shaped like a parabola. After t seconds, its height above sea level in meters is modeled by the function h(t) = t2 – 10.2t + 18. After how many seconds does the ball reach its minimum height? What is that minimum height? Round your answers to the nearest hundredth’s place; use proper units in your answer.
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h(t) = t^2 – 10.2t + 18
Because the coeeficient associated with the t^2 term is positive, we know it is a parabola that opens upwards.
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Thus, the vertex gives you the maximun:
After how many seconds does the ball reach its minimum height?
t = -b/(2a) = -(-10.2)/(2*1) = 10.2/2 = 5.1 secs
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What is that minimum height?
Now that we know the time (secs) we plug it back in to:
h(t) = t^2 – 10.2t + 18
h(5.1) = 5.1^2 – 10.2(5.1) + 18
h(5.1) = 26.01 – 52.02 + 18
h(5.1) = -8.01 meters

SOLUTION: A tennis ball is rolled down a valley along a slope shaped like a parabola. After t seconds, its height above sea level in meters is modeled by the function h(t) = t2 – 10.2t + 18.