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Burka [1]
3 years ago
6

The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 7 feet, represented by a ve

rtex of (4,7)
, and lands 8 feet from the water jet, represented by (8,0)
. Write a function in vertex form that models the path of the stream.

Mathematics
1 answer:
xenn [34]3 years ago
3 0

First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.

If we need the vertex to be at x=4, the equation will contain a (x-4)^2 term.

If we start with y=-(x-4)^2 we have a parabola, concave down, with vertex at x=4 and a maximum of 0.

So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be (4, 7)

We have

y = -(x-4)+7

Now we only have to fix the fact that this parabola doesn't land at (8,0), because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want

y = a(x-4)^2+7

such that:

  • a
  • when we plug x=8, we have y=0

Plugging these values gets us

0 = a(8-4)^2+7 \iff 16a+7=0 \iff a = -\dfrac{7}{16}

As you can see in the attached figure, the parabola we get satisfies all the requests.

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Answer:

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Step-by-step explanation:

What we have to know is that when two triangles are similar their sides will always be proportional. So we will create a proportion that goes like this...\frac{\Delta1side}{\Delta1base} =\frac{\Delta2side}{\Delta2base} but since it doesn't tell us the exact value of triangle 1. We will have to add 3 and 12 to get 15 which is the base of the first triangle. Now we're ready to write the proportion.

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Now we cross multiply and solve the equation...

48x=15(3x+1)\\48x=45x+15\\3x=15\\x=5

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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