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Nataliya [291]
3 years ago
7

The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the

spout in feet. Complete the square to determine the maximum height of the path of the water.
−4(x − 3)2 − 29; The maximum height of the water is 3 feet.

−4(x − 3)2 − 29; The maximum height of the water is 29 feet.

−4(x − 3)2 + 7; The maximum height of the water is 7 feet.

−4(x − 3)2 + 7; The maximum height of the water is 3 feet.
Mathematics
2 answers:
kirza4 [7]3 years ago
8 0
Below is the solution:

f(x)=−4(x2−6x+9−9)−29

<span> (</span>x2−6x+9)=(x−3)(x−3)

f(x)=−4((x−3)2−9)−29

f(x)=−4(x−3)2−4(−9)−29

f(x)=−4(x−3)2+36−29

f(x=−4(x−3)2+7

f(x)=−4(x−3)2+7

That's the equation we got by completing the square.

y=a(x−h)2+k

That's the formula of a parabola in "vertex" form. Notice the similarity? The two are equal if we say

y=f(x)

a=−4

h=3

k=7


Therefore the answer is C, <span>−4(x − 3)2 + 7; The maximum height of the water is 7 feet.</span>


attashe74 [19]3 years ago
7 0

Answer:

Option 3 - y= -4(x-3)^2+7; The maximum height of the water is 7 feet.

Step-by-step explanation:

Given : The height of water shooting from a fountain is modeled by the function f(x) = -4x^2+24x-29 where x is the distance from the spout in feet.

To find : Complete the square to determine the maximum height of the path of the water.

Solution :

f(x) = -4x^2+24x-29

f(x) = -4(x^2-6x)-29

Completing the square by adding and subtracting (\frac{6}{2})^2=3^2=9 in the bracket,

f(x) = -4(x^2-6x+9-9)-29

f(x) = -4((x-3)^2-9)-29

f(x) = -4(x-3)^2+36-29

f(x) = -4(x-3)^2+7

The general vertex form is y=a(x-h)^2+k

On comparing,

a=−4, h=3, k=7

The maximum height of the water is given by y-intercept i.e. k,

The maximum height of the water is 7 feet.

Therefore, Option 3 is correct.

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Salutations!

Mark got 20% raise for his salary. If this salary was $1800 what is the new salary?

So lets solve this!

Mark got 20% "raise" for his salary. It clearly indicates that it is percentage of increase, so therefore, after solving out all the sum, we would be adding up 1800 to get the total of the new salary.

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Learn more about speed at:

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