Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisHard

A physics student recorded the height of a ball at several times after it was launched upward. A quadratic model that fits the data is h=−4.9t2+19.6t+1.5h = -4.9t^2 + 19.6t + 1.5, where hh is the height, in meters, tt seconds after launch. According to the model, what is the maximum height, in meters, of the ball?

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Answer: 21.1

For a quadratic at2+bt+cat^2 + bt + c with a<0a < 0, the maximum occurs at t=−b2a=−19.62(−4.9)=2t = -\frac{b}{2a} = -\frac{19.6}{2(-4.9)} = 2 seconds. Substituting, h=−4.9(4)+19.6(2)+1.5=−19.6+39.2+1.5=21.1h = -4.9(4) + 19.6(2) + 1.5 = -19.6 + 39.2 + 1.5 = 21.1 meters.

Answering 22 gives the time at which the maximum occurs, not the maximum height.

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