Question

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

Answer 1

If 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.

Answer 2

that is the rule.....

Answer 3

Ok so the first one would be that it opens down correct?

Answer 4

thank-you:) Can I ask anither?

Answer 5

yes, the first one opens down. Right;)

Answer 6

And the second one opens where?

Answer 7

(and yes, you can ask another question right here, after you feel that you are done with this question.)

Answer 8

It opens us since it's poitive

Answer 9

yes

Answer 10

ok i guess you are done with this question... r u?

Answer 11

do you have any questions about this question ?

Answer 12

so the first one, is opening down w/ the vertex at an absolute maximum? I'm just checking

Answer 13

yes

Answer 14

the vertex in function 1 is absolute maximum

Answer 15

Ok thank-you:)

Answer 16

Suppose 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

Answer 17

yw

Answer 18

i don't understand this one

Answer 19

you don't understand the question, or don't know how to solve it?

Answer 20

I don't understand how to solve it

Answer 21

oh....ok...

Answer 22

I 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?

Answer 23

yes. Yes I do

Answer 24

Now, 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

Answer 25

(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

Answer 26

2(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.

Answer 27

the last option is going to be obviously smaller than or greater than the 3rd option ?

Answer 28

can you tell me?

Answer 29

so the answer would be c2+d2

Answer 30

hold on...

Answer 31

pliz answer my last question...

Answer 32

(you are trying to jump ahead to quickly:o)

Answer 33

smalleer :) Sorry

Answer 34

yes (no need for apologies).

Answer 35

So, 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).

Answer 36

((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)

Answer 37

The 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?

Answer 38

)c+d)^2

Answer 39

Yes, (C+D)² is the largest, and this it is the answer you need:)

Answer 40

Any questions about this problem?

Answer 41

No. :)

Answer 42

OK.....

Answer 43

Three 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

Answer 44

ok, this is a last question for this post. Alright>

Answer 45

Yea:)

Answer 46

h(x) = ?

Answer 47

h(x): graph parabola (1,-3) (3,5) (-1,5)

Answer 48

for h(x), if you were to graph the points: