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mote1985 [20]
3 years ago
14

The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 12 feet, represented by a v

ertex of (8,12)​ , and lands 16 feet from the water jet, represented by (16,0)​ . Write a function in vertex form that models the path of the stream
Mathematics
2 answers:
tia_tia [17]3 years ago
8 0

Answer:

y=-3/16(x-8)^2+12

Step-by-step explanation:

Refer to the vertex form equation for a parabola:

y=a(x-h)^2+k where (h,k) is the vertex.

Therefore, we have y=a(x-8)^2+12 as our equation so far. If we plug in (16,0) we can find a:

0=a(16-8)^2+12

0=64a+12

-12=64a

-12/64=a

-3/16=a

Therefore, your final equation is y=-3/16(x-8)^2+12

Stels [109]3 years ago
7 0

Answer:

y = (-5.33)(x - 8)^2 + 12

Step-by-step explanation:

The graph is a parabola which opens down and has its vertex at (8, 12).  We can immediately write y = a(x - 8)^2 + 12, knowing that if x = 8, y = 12.  To find the coefficient '1', substitute 16 for x and 0 for y:

0 = a(16 - 8)^2 + 12, or

-64a = 12, or a = -64/12 = 5.33

Then the desired function is:

y = (-5.33)(x - 8)^2 + 12

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Answer:

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Step-by-step explanation:

So It most likely adds up to 180 degrees so.

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x = 47

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3 years ago
Complete the square to rewrite y-x^2-6x+14 in vertex form. then state whether the vertex is a maximum or minimum and give its co
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Answer:

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And solving we have:

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The vertex for this case would be:

V= (3,5)

And the minimum for the function would be 3 and there is no maximum value for the function

Step-by-step explanation:

For this case we have the following equation given:

y= x^2 -6x +14

We can complete the square like this:

y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2

And solving we have:

y= x^2 -6x +9 + 14 -9

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And we can write the expression like this:

y-5 = (x-3)^2

The vertex for this case would be:

V= (3,5)

And the minimum for the function would be 3 and there is no maximum value for the function

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Step-by-step explanation:

200 m is only 0.12 miles

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Step-by-step explanation:

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