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Word problem involving the maximum or minimum of a quadratic function

Word problem involving the maximum or minimum of a quadratic function-example-1
User Jay Dansand
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1 Answer

20 votes
20 votes

Given the function of the height of the ball thrown vertically upward as;


h(t)=44t-16t^2

Where t is time taken it takes to get to the height.

The graph of the quadratic function is;

Thus, it has a maximum height.

At the maximum height;


(dh(t))/(dt)=0

Thus,


\begin{gathered} (dh(t))/(dt)=(d(44t-16t^2))/(dt)=0 \\ 44-32t=0 \\ 32t=44 \\ t=(44)/(32) \\ t=1.375\sec s \end{gathered}

Now, we can get the maximum height at t = 1.375 seconds. We have;


\begin{gathered} h(1.375)=44(1.375)-16(1.375)^2 \\ h(1.375)=60.5-30.25 \\ h(1.375)=30.25 \end{gathered}

The maximum height the ball will reach is 30.25 feets.

Word problem involving the maximum or minimum of a quadratic function-example-1
User Martyglaubitz
by
2.7k points
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