iwillrektyou
  • iwillrektyou
1. 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. (2 points) −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. 2. In the function f(x) = 4(x2 − 6x + [blank] ) + 20, what number belongs in the blank to complete the square?
Mathematics
katieb
  • katieb
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iwillrektyou
  • iwillrektyou
For #2, I think the blank is 9, for #1, I'm totally confused.
Jhannybean
  • Jhannybean
\[f(x)=-4x^2+24x-29\] in the method of completing the square, this is how I would go about solving it. first group your x-terms together. \((-4x^2+24x)-29\) Now out of the grouped x-terms, factor out the LCM, -4.: \(-4(x^2-6x)-29\) We complete the square inside the parenthesis. therefore we need to find a new "c" value. \(c= \left(\dfrac{-6}{2}\right)^2 = (-3)^2 = 9\) plug this back in to the parenthesis to complete the quadratic form, \(ax^2+bx+c\) \(-4(x^2-6x+9)-29\) Now this is the problem child, a lot of people forget that whatever you do inside the ( ), you `must also do outside the ( )`. Because we added `+9` inside the parenthesis, we will have to `subtract` the equivalent. That is, \((-4 \cdot 9) = -36\)\[-4(x^2-6x+9)-29-(-36)\]\[-4(x^2-6x+9)-29+36\]\[-4(x^2-6x+9)+7\] Now we must simplify the stuff in ( ) because it is a perfect square after all. \[\color{red}{\boxed{-4(x-3)^2+7}}\]
iwillrektyou
  • iwillrektyou
Thank you so much! Can you please check if 9 is the answer to #2?

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iwillrektyou
  • iwillrektyou
And for the first problem, the vertex is (3, 7), so is the maximum height 3 feet?
Jhannybean
  • Jhannybean
The maximum `height` in correlated to the `y-value`
iwillrektyou
  • iwillrektyou
So it is 7?
Jhannybean
  • Jhannybean
Yes
iwillrektyou
  • iwillrektyou
Thank you very much.
Jhannybean
  • Jhannybean
Do you understand how I went about solving it? @iwillrektyou
iwillrektyou
  • iwillrektyou
Yes, I also did it on my paper and got the same answer. For #2, I got 9, using the middle coefficient. 6/2 = 3 ; 3^2 = 9
Jhannybean
  • Jhannybean
yes that is correct. (-6/2)^2 = (-3)^2 = 9 \(\checkmark\)
iwillrektyou
  • iwillrektyou
Would you mind helping me with a few more?
Jhannybean
  • Jhannybean
i've actually got to head off and work on my own homework, so im sorry about that!
iwillrektyou
  • iwillrektyou
Thank you so much for your time and patience!
Jhannybean
  • Jhannybean
No problem :)

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