## iwillrektyou one year ago 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?

1. iwillrektyou

For #2, I think the blank is 9, for #1, I'm totally confused.

2. anonymous

$f(x)=-4x^2+24x-29$ 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. $\color{red}{\boxed{-4(x-3)^2+7}}$

3. iwillrektyou

Thank you so much! Can you please check if 9 is the answer to #2?

4. iwillrektyou

And for the first problem, the vertex is (3, 7), so is the maximum height 3 feet?

5. anonymous

The maximum height in correlated to the y-value

6. iwillrektyou

So it is 7?

7. anonymous

Yes

8. iwillrektyou

Thank you very much.

9. anonymous

Do you understand how I went about solving it? @iwillrektyou

10. 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

11. anonymous

yes that is correct. (-6/2)^2 = (-3)^2 = 9 $$\checkmark$$

12. iwillrektyou

Would you mind helping me with a few more?

13. anonymous

i've actually got to head off and work on my own homework, so im sorry about that!

14. iwillrektyou

Thank you so much for your time and patience!

15. anonymous

No problem :)