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anonymous
 one year ago
The functions f(x) = –(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completingthesquare method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.
anonymous
 one year ago
The functions f(x) = –(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completingthesquare method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1If your quadratic has a negative leading coefficient, then it opens down, and its vertex is the aboslute maximum. If your quadratic has a positive leading coefficient, then it opens up, and its vertex is the absolute minimum.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1that is the rule.....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok so the first one would be that it opens down correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thankyou:) Can I ask anither?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, the first one opens down. Right;)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And the second one opens where?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(and yes, you can ask another question right here, after you feel that you are done with this question.)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It opens us since it's poitive

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1ok i guess you are done with this question... r u?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1do you have any questions about this question ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the first one, is opening down w/ the vertex at an absolute maximum? I'm just checking

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1the vertex in function 1 is absolute maximum

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Suppose C and D represent two different school populations where C > D and C and D must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary. (C + D)2 2(C + D) C2 + D2 C2 − D2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i don't understand this one

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you don't understand the question, or don't know how to solve it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand how to solve it

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I will also add, that C and D must be integers (since you can't have 3.5 people of anything like that).... do you agree with me?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now, C is at least 1. D is at least 2. (So, C+D is at least 3) Which is the largest? Explain why. Show all work necessary. (C + D)² 2(C + D) C² + D² C² − D²

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(C+D)² when C=1 & D=@ is going to be (1+2)²=3²=9 2(C+D) 2(1+2)=2(3)=6

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.12(C+D) is a linear growth, and (C+D)² is a "quadratic" growth. And the bigger "C+D" we have the greater will (C+D) get when compared to (C+D) that will not grow even nearly as rapidly.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1the last option is going to be obviously smaller than or greater than the 3rd option ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1can you tell me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer would be c2+d2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1pliz answer my last question...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(you are trying to jump ahead to quickly:o)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes (no need for apologies).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, the last option falls off... and in competition is the 1st option (C+D)² which is larger than the 2nd option (as i showed), and the 3rd option (which is obviously larger than the 4th option).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1((remember D must be greater than C, and both C and D are natural numbers)) C²+D² vs (C+D)² DIFFERENCE  C=1 & D=2 1²+2²=5 vs (1+2)²=9 (C+D)² exceeds by 4  C=1 & D=3 1²+3²=10 vs (1+3)²=16 (C+D)² exceeds by 6  C=2 & D=3 2²+3²=13 vs (2+3)²=25 (C+D)² exceeds by 12  C=2 & D=4 2²+4²=18 vs (2+4)²=36 (C+D)² exceeds by 18 (& twice)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The greater values for C and D we pick, the more (C+D)² exceeds, (outmatches if you will) the C²+D². So which one is the largest?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, (C+D)² is the largest, and this it is the answer you need:)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Any questions about this problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest). f(x) g(x) h(x) f(x) = 3(x + 4)2 + 1 g(x) = 2x2 − 16x + 15

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1ok, this is a last question for this post. Alright>

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0h(x): graph parabola (1,3) (3,5) (1,5)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1for h(x), if you were to graph the points:dw:1435801328063:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you can tell that (1,3) is the vertex od the parabola.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And that way we know that \(\Large y=\color{red}{\rm a}(x1)^23\) part.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1we know everything besides the scale factor (or the coefficient) we will use.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(btw, if you don't undertsnad something completely, you are welcome to ask anything that you would like)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. I understand everything so far. No worries:)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, yes... so now we need to use one of your point. We know that this parabola should satisfy the point (3,5)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1don't forget that this parabola that we are finding is the h(x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, \(\large\color{black}{ \displaystyle h(x)=\color{red}{\rm a}(x1)^23 }\) we know that point (3,5) should be on the parabola. So: \(\large\color{black}{ \displaystyle \color{blue}{5}=\color{red}{\rm a}(\color{blue}{3}1)^23 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Can you solve for a, please?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman is it g(x), f(x), and then h(x) ? I'm sorry

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle \color{blue}{5}=\color{red}{\rm a}(\color{blue}{3}1)^23 }\) \(\large\color{black}{ \displaystyle \color{blue}{5}=\color{red}{\rm a}(2)^23 }\) \(\large\color{black}{ \displaystyle \color{blue}{5}=4\color{red}{\rm a}3 }\) \(\large\color{black}{ \displaystyle 2=4\color{red}{\rm a} }\) a=½

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this a that we found, we found for h(x).....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, \(\large\color{black}{ \displaystyle f(x) = 3(x + 4)^2 + 1 }\) \(\large\color{black}{ \displaystyle g(x) = 2x^2 − 16x + 15 }\) \(\large\color{black}{ \displaystyle h(x) = \frac{1}{2}(x 1)^2 3 }\) (we foudn a=1/2)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and xaxis of summetry (in this case) is just the xcoordinate of the vertex.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1just "axis of summetry" (not "xaxis of summetry")

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you need to complete the square for g(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, h(x) axis of symmetry would be 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman I have no idea how to do that

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes for h(x) it is 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1can you identify the axis of summetry for f(x) ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now, for g(x). \(\large\color{black}{ \displaystyle g(x)=2x^216x+15 }\) \(\large\color{black}{ \displaystyle g(x)=2(x^28x)+15 }\) following so far?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1we will do g(x)... do you undertsand my previousppost?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok. \(\large\color{black}{ \displaystyle g(x)=2(x^28x)+15 }\) what would you want to have added inside the parenthesis ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1what number do you need to add \(\large\color{black}{ \displaystyle g(x)=2(x^28x~+\color{blue}{\bf here} )+15 }\) to make the part in the parenthesis a perfect square trinomial ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1when you have \(x^2bx\) the number that you would like to add is \((b/2)^2\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1in this case (8/2)² > 4² > 16

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So we would like to add 16, but we can't just add numbers, we are going to change the value of the function....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1How would we add the number without changing the value of the function? like this....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\LARGE \color{black}{ \displaystyle g(x)=2(x^28x\color{blue}{+16}\color{red}{16})+15 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So far I haven't changed anything, I just added a "magic zero"

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now, expand the 16 (in red) out of parenthesis \(\LARGE \color{black}{ \displaystyle g(x)=2(x^28x\color{blue}{+16})+2\cdot (\color{red}{16})+15 }\) \(\LARGE \color{black}{ \displaystyle g(x)=2(x^28x\color{blue}{+16})32+15 }\) \(\LARGE \color{black}{ \displaystyle g(x)=2(x^28x\color{blue}{+16})17 }\) \(\LARGE \color{black}{ \displaystyle g(x)=2(x4)^217 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1so what is the axis of summetry for g(x) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would be f(x), hx, gx

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, now you need to list all axis of summetry in order from smallest to greatest.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes. f , h, g. 4, 1, 4.
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