Question

Help pleaseee!

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.

Answer 1

@mathmale

Answer 2

chitty chitty @bangbang559

Answer 3

what?

Answer 4

http://www.imdb.com/title/tt0062803/

Answer 5

its C

Answer 6

how do you know?

Answer 7

@hoblos

Answer 8

@zepdrix

@ganeshie8

Answer 9

@whpalmer4

Answer 10

Come on back, and I'll work the problem with you...

Answer 11

here

Answer 12

\[f(x) =−4x^2 + 24x − 29\]We need to complete the square. I would start by factoring out the -4:

\[-4(x^2-6x-\frac{29}{4})\]Do you agree with that result so far?

Answer 13

Actually, let me write it slightly differently:
\[f(x) = -4(x^2-6x) -29\]

Answer 14

yup

Answer 15

Okay. Now to complete the square, we take half of the coefficient of \(x\), and square it. \[(\frac{-6}{2})^2 = (-3)^2 = 9\]We are going to simultaneously add and subtract that inside the parentheses. \(9-9=0\) so we are not changing the value of anything.
\[f(x) = -4(x^2 -6x +9 - 9) - 29\]Now, we can rewrite \[(x^2-6x+9) = (x-3)(x-3)\]\[f(x) = -4((x-3)^2 -9) - 29\]We apply the distributive property:
\[f(x) = -4(x-3)^2 -4(-9) - 29\]\[f(x) = -4(x-3)^2+36-29\]\[f(x = -4(x-3)^2+7\]Any questions about what I did?

Answer 16

That last line should be \[f(x) =-4(x-3)^2+7\]

Answer 17

Vertex form for a parabola is \[y = a(x-h)^2+k\]where the vertex is located at \((h,k)\)
Can you tell me the vertex of this parabola?

Answer 18

this really confuses me

Answer 19

What does, the completing of the square, or vertex form, or both?

Answer 20

a new equation

Answer 21

which new equation are you talking about?

Answer 22

\[f(x) = -4(x-3)^2 + 7\]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, our parabola has a vertex of \((3,7)\). As \(a < 0\), that parabola opens downward, and the vertex will be at the highest point. Therefore, the maximum height of the water is 7 feet, which is the y value of the vertex.

Answer 23

A plot of the function is attached, where you can clearly see that the vertex is at (3,7).