Question

PLEASE HELP FAN AND MEDAL IN RETURN I NEED HELP I NEED TO GET THIS DONE PLEASE HELP!!

Answer 1

whats the question

Answer 2

This project may be completed individually or collaboratively.

The town of West Mathington needs help planning some roads that will connect parts of their fair city. The town of West Mathington is laid out so that North is the positive y-axis, and East is the positive x-axis. The roads will follow the paths of graphs created from linear, quadratic, and exponential functions.

These samples provided will give you an idea of what a final map could look like.

Answer 3

http://learn.flvs.net/webdav/educator_algebraI_v17/module09/images/09_06_assessment/09_06_assessment_01.jpg

Answer 4

http://learn.flvs.net/webdav/educator_algebraI_v17/module09/images/09_06_assessment/09_06_assessment_02.jpg

Answer 5

1. West Mathington’s most urgent need is a parabolic freeway. Create your own upward opening quadratic function, f(x), which has two real zeros. Prove that f(x) has two real zeros.

2. Two on-ramps need to be placed on the parabolic freeway. Decide where on the parabola of f(x) you are placing the on-ramp locations. Write those ordered pairs down.


3. West Mathington wants to connect these on-ramps with some surface roads.
Create a linear growth function, h(x), that passes through both on-ramp points.
Create an exponential growth function, j(x), that passes through at least one of the on-ramp points.

Show all of the work you did to create both functions.



4. What important relationship do the x-coordinates of the on-ramp location points have with the system of equations formed by the two roads’ functions that are being connected? Provide justification and support for your explanation.

5. The city planner needs to identify the most northern road. Prove which road will eventually go the furthest to the north (positive y-direction). Create tables for your functions using an appropriate domain of five integers. Using the tables and graph, explain to the city planner which road will be the furthest north as the x-values continue to get larger (the road continues to go east). Provide reasoning why.


6.Include your graph that shows the functions that model each of the roads and the on-ramps.

Answer 6

don't mind the question marks they aren't anything

Answer 7

ok do you know how to create a function with 2 zeros?

Answer 8

choose 2 points you like on the x-axis for your zeros

Answer 9

i made this, for #1 f(x)=x^2-1
0=x^2-1,
so (1,0) and (-1,0)

Answer 10

nope that wouldn't work because it doesn't have zeros on the x axis

Answer 11

oh

Answer 12

Can you help me make one or can i adjust that one a little?

Answer 13

nevermind it does work

Answer 14

ok :)

Answer 15

so #1 is done right

Answer 16

yup

Answer 17

Ok on to #2

Answer 18

This is what I did

Answer 19

f(3)= 3^2-1 = 8
(3,8)

f(4)= 4^2-1 = 15
(4,15)

Answer 20

ok

Answer 21

so that works?

Answer 22

ya but its gonna be up there

Answer 23

oh ok should we bring down the numbers to something else 1 and 2 maybe? or 2 and 3?

Answer 24

that would be nice

Answer 25

which one?

Answer 26

I would chose like x=-1 and x=2 depends how the freeway you want

Answer 27

Ok i will do that.

Answer 28

since the zeros were the surface

Answer 29

i get 0 for f(-1)

Answer 30

yes

Answer 31

ok and 3 for f(-2)

Answer 32

yup

Answer 33

ok

Answer 34

So write those ordered pairs down

Answer 35

Ok.

Answer 36

(-1, 0) and (2,3)

Answer 37

Ok so that is #2 onto number 3

Answer 38

h(x) is the equation of a line that passes through your 2 points

Answer 39

Where'd u go :(

Answer 40

Ok how about,

h(x) = 2x+7

Answer 41

which points are you using ?

Answer 42

hmm

(-1,0) and (2,3)

Answer 43

look above please so you can see where we are at it will help a lot

Answer 44

thx for staying and helping

Answer 45

I would find the slope between those two points: change in y divided by change in x

Answer 46

ok.

Answer 47

is it 3?

Answer 48

3-0
____
2-1

Answer 49

almost. the bottom is 2 - (-1) right ?

Answer 50

Oh yes my bad the two minuses

Answer 51

so its 1

3
__
3

Answer 52

yes, so the equation is
y = 1x + b or just
y= x+b
now replace x and y with one of the points (-1,0) for example and find b

Answer 53

hmmm ok

Answer 54

-1=0+b

Answer 55

b=-1

Answer 56

I think x=-1 and y is 0 in (-1,0)
you did it the other way round.

Answer 57

Oh

Answer 58

ok

0=-1+b

Answer 59

b=1

Answer 60

@phi

Answer 61

so the equation is
y= x+1
let's test: (-1,0) should be "on the line"
y= -1+1 = 0 which is correct
now check (2,3)
y= 2+1= 3, and that is good.

Answer 62

ok

Answer 63

So #3 is done right?

Answer 64

you found h(x)= x+1

but wait, there is more:
Create an exponential growth function, j(x), that passes through at least one of the on-ramp points.

Answer 65

ok

Answer 66

j(x)=2x^2+4

Answer 67

actually no that won't work

Answer 68

which point do you want to go through?

Answer 69

can i go through (2,3)

Answer 70

ok

remember
exponential growth function means base^x
I would use 2 for the base (it's simple)
so
y= 2^x + B
we replace x and y with 2 and 3, and find B

Answer 71

Ok

Answer 72

3=2^2+b
b=-1

Answer 73

so what equation do you get?

Answer 74

3=2x^2-1?

Answer 75

first, the equation has a y (or in this case , j(x) ) not a 3
also, exponential means x is an exponent.
x^2 is a parabola or quadratic which is different.

can you try again ?

Answer 76

ok

Answer 77

use the equation I posted up above, but replace B with -1

Answer 78

j(x) =2^2-1?

Answer 79

closer, but we need x as the exponent not 2 (we used x=2 so we could find B, but now we leave it x)

Answer 80

ok

j(x)=2^x-1

Answer 81

yes. this equation has an x that we "replace" with a number to find the y
for example, when x is 2 we get j(2) = 2^2-1 = 4-1= 3 (as we should)
but we can get other points: when x is 0 we get j(0) = 2^0 - 1 = 1-1 = 0
and so on...

Answer 82

ok

Answer 83

Ok i understand that :)

Answer 84

@phi still here? :(

Answer 85

yes.

Answer 86

ok thx for sticking with me

Answer 87

You can use geogebra to plot your equations

Answer 88

ok is that for #3?

Answer 89

yes

Answer 90

Ok

Answer 91

so #4 this is where i have no idea what to do.

Answer 92

4. What important relationship do the x-coordinates of the on-ramp location points have with the system of equations formed by the two roads’ functions that are being connected? Provide justification and support for your explanation.

Answer 93

can you see the plot I posted. the x coordinate of the point A (-1,0)
is the solution to the system of equations: parabola and line
the x value of point B is the solution to the system with parabola, line and exponential

Answer 94

yes i can

Answer 95

so that is the answer to 4 right
what u wrote

Answer 96

yes, but you can write in the equations (not just the names)

Answer 97

can you explain or write it like that for me

i don't know what you mean