Question

Can someone please help me, I have been waiting for help for almost an hour. Please help

Answer 1

What's your question?

Answer 2

In 2005, some data was taken on the number of women in certain age groups who gave birth.?
Age of Women 22 27 32

Number of women per 102 116 96

1000 who gave birth

a)determain f(x)=a(x-h)^2+k,so that f model this data(not ax^2+bx+c)(Use trial and error, and find values of a, h, and k to the tenths place to guarantee that your
graph comes close enough to “go through” all 3 points on the table when on “ZOOM STAT”
[as boxes in the TI-83/84].)


(b) Estimate the number of women per 1000 who give birth at age 35 according to your model


(c) Where does it look like f (x)=0 ? (You will likely need to expand your window, especially
since you used “ZoomStat”.)

What does this mean? Do you believe this? Is f(x)a perfect model of what really happens?
(answer all 3 questions)

Answer 3

Shoot, I don't have a graphing calculator with me. Sorry! I could help you do it by hand, but it'll take a lot longer.

Answer 4

thats ok, I have an exam on this so i would like to learn it by hand or calculator , if you can?

Answer 5

Alright. Your coordinates are (22, 102), (27, 116), and (32, 96). Your general form is going to be y = ax^2 + bx + c.

Answer 6

he said Not ax^2 +bx+c

Answer 7

Yeah, but this is the only way I know how to do it by hand. Your graphing calculator is set up to put it into the other form.

Answer 8

oh ok

Answer 9

The first step is to determine your equations. Take the first point (22, 102). 22 is the x-coordinate, so you're going to substitute 22 for x. The y-coordinate is 102. Substitute that for y. You get
\[102 = a*22^2+b*22+c\]

Answer 10

Okay with that?

Answer 11

yes

Answer 12

*What level of math are you at?

Answer 13

95

Answer 14

Roughly Intermediate Algebra?

Answer 15

yes

Answer 16

So this equation simplifies this way
102 = 484a + 22b + c

Answer 17

Try finding the equation for the second point.

Answer 18

116=729a+27b+c ?

Answer 19

Yep, good :).
Third one?

Answer 20

96=1024a+32b+c

Answer 21

Good. Now we have our three equations:
102 = 484a + 22b + c
116 = 729a + 27b + c
96 = 1024a + 32b + c

Let's take the first equation. 102 = 484a +22b + c. Solve that for c. What do you get?

Answer 22

can you show me the first one

Answer 23

Sure. We want c, so we have to get rid of 484a and 22b.

Subtract 484a from both sides to get
-484a + 102 = 22b + c

Okay with that step?

Answer 24

would you also subtract 48 from the other side

Answer 25

484a? Yes, but I already took it off.

Answer 26

102 - 484a = 484a - 484a +22b + c

Answer 27

-484a + 102 = 22b + c

Answer 28

ok i’m sorry i am soo lost

Answer 29

when i did it using the Ti-83 i got a=-.68 h-26.56 k=116.13

Answer 30

No worries. We start with this:
102 = 484a + 22b + c

Subtract 484a from both sides:
102 = 484a + 22b + c
-484a -484a

-484a +102 = 0a + 22b + c
-484a +102 = 22b +c

Answer 31

OH, missed your last message.

Answer 32

That makes it much easier.

Answer 33

So you have f(x) = a(x-h)^2 + k

Substitute your values:
f(x) = -0.68(x - 26.56)^2 + 116.13

Answer 34

That function is a model for your data.

Answer 35

where i am stuck at is part b: Estimate the number of women per 1000 who give birth at age 35 according to your model.

Answer 36

What does x represent in your model?

Answer 37

If you understand that, then the problem will be easy.

Answer 38

age of women i think

Answer 39

Yep. Which is 35 in this case. Just plug that into x and whatever comes out will be your answer.

Answer 40

f(35) = -0.68(35 - 26.56)^2 + 116.13

Answer 41

67.691152?

Answer 42

Yep :)

Answer 43

ok so what other part of the question is what does this mean? do you belive this? Is f(x) a perfect model of what really happens?

Answer 44

Well, the model they chose for this is a quadratic equation, which doesn't really make sense. There's not really any reason to suspect that it would be a quadratic equation, but it would probably approximate it pretty well for a small area of the data.

Answer 45

Also, it will dip below zero eventually, which doesn't make sense either.

Answer 46

where does it look like f(x)=0

Answer 47

That's where it hits the x-axis. Zoom out until you see it hit the axis.

Answer 48

thank you so much, you made it clear to understand the steps

Answer 49

No problem :) . Have a good night.

Answer 50

thanks you too