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)=t^2-8.9t+14. After

Algebra ->  Equations -> 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)=t^2-8.9t+14. After      Log On


   

Question 368989: 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)=t^2-8.9t+14. After how many seconds does the ball reach its minimum height? What is that minimum height? Round to the nearest hundredths place and use proper units in your answer.
Found 2 solutions by Alan3354, nerdybill:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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)=t^2-8.9t+14. After how many seconds does the ball reach its minimum height? What is that minimum height?
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The min height is at the vertex of the parabola, which is on the line of symmetry, at t = -b/2a = 8.9/2
t = 4.45 seconds.
min = h(4.45) = 4.45^2 - 8.9*4.45 + 14
min =~ -5.803 meters

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
h(t)=t^2-8.9t+14
.
We know it is a "quadratic" because it is in the form of:
Ax^2 + Bx + C
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Looking at the coefficient associated with the t^2 term, since it is positive (happy face) the parabola opens upwards. The vertex will give you the minimum.
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After how many seconds does the ball reach its minimum height?
t = -b/(2a)
t = -(-8.9)/(2*1)
t = (8.9)/2
t = 4.45 secs
.
What is that minimum height?
Plug the value above back into:
h(t)=t^2-8.9t+14
h(4.45)=4.45^2-8.9(4.45)+14
h(4.45)= -5.80 meters