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Evgesh-ka [11]
2 years ago
15

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What i

s the maximum height that the ball will reach?
Do not round your answer.
Mathematics
2 answers:
babunello [35]2 years ago
6 0

Answer:

42.25 feet

Step-by-step explanation:

The maximum of a quadratic can be found by finding the vertex of the parabola that the quadratic creates visually on a graph.

So first step to find the maximum height is to find the x-coordinate of the vertex.

After you find the x-coordinate of the vertex, you will want to find the y that corresponds by using the given equation, y=52x-16x^2. The y-coordinate we will get will be the maximum height.

Let's start.

The x-coordinate of the vertex is \frac{-b}{2a}.

y=52x-16x^2 compare to y=ax^2+bx+c.

We have that a=-16,b=52,c=0.

Let's plug into  \frac{-b}{2a} with those values.

\frac{-b}{2a} with a=-16,b=52,c=0

\frac{-52}{2(-16)}=\frac{52}{32}=\frac{26}{16}=\frac{13}{8}.

The vertex's x-coordinate is 13/8.

Now to find the corresponding y-coordinate.

y=52(\frac{13}{8})-16(\frac{13}{8})^2

I'm going to just put this in the calculator:

y=\frac{169}{4} \text{ or } 42.25

So the maximum is 42.25 feet.

Nata [24]2 years ago
4 0

Answer: 42.25 feet

Step-by-step explanation:

We know that after "t" seconds, its height "h" in feet is given by this function:

h(t) = 52t -16t^2

The maximum height is the y-coordinate of the vertex of the parabola. Then, we can use the following formula to find the corresponding value of "t" (which is the x-coordinate of the vertex):

x=t=\frac{-b}{2a}

In this case:

a=-16\\b=52

Substituting values, we get :

t=\frac{-52}{2(-16)}\\\\t=1.625

Substituting this value into the function to find the maximum height the ball will reach, we get:

h(1.625) = 52(1.625) -16(1.625)^2\\\\h(1.625) =42.25\ ft

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