Question

I need help on a assignment!

Answer 1

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.

I did those but I need help on the rest!

Answer 2

I need help on 4 and 5

Answer 3

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.

Answer 4

@triciaal

Answer 5

2 real zeros when b^2 = 4 a c from the general equation ax^2 + bx + c = 0

Answer 6

wait how would i explain it for number 4?

Answer 7

upward opening means a is positive

Answer 8

I did 1-3. I just need some help on 4 and 5

Answer 9

show what you have then

Answer 10

ok hang on one sec

Answer 11

@peachpi @sleepyjess @Data_LG2

Answer 12

1. f(x) = x^2 - 1

2. I got the points (-1,0) and (2,3)

3. linear function: y=x+1
exponential function: f(x) = 2^x -1

Answer 13

@Michele_Laino please help

Answer 14

@triciaal where are you going??

Answer 15

@sleepyjess @Michele_Laino

Answer 16

It seems that your answer is right!

Answer 17

thanks! umm im just confused about 4 and 5 though can you help? @Michele_Laino

Answer 18

I think that we have to write the function of each on-ramp

Answer 19

ok would i say that the important relationship the x-coordinates of the on-ramp location points have with the system of equations is that the freeway and roads become connected? I would provide justification and support for your explanation by showing the graph and label everything? for number 4

Answer 20

@Michele_Laino

Answer 21

yes! I think so!

Answer 22

ok thanks! what about number 5??

Answer 23

how would i make the tables?

Answer 24

for part #5, we have to construct those two on-ramps

Answer 25

how would i do that

Answer 26

one on-ramp has to pass at point (-1,0), and the other one has to pass at point (2,3). Furthermore both on-ramp have to be represented by a straight line, so the corresponding function has to be like this:
y= a*x+b

Answer 27

wait i already did that? number 5 wants a table how do i do that?

Answer 28

I think that one on-ramp can be represented by this function:
\[y = \frac{1}{2}\left( {x + 1} \right)\]

Answer 29

i'm confused now?

Answer 30

and the second one, can be represented by this function:
\[y = - x + 5\]

Answer 31

for number 5? arent they asking for a table though

Answer 32

I know, nevertheless in order to write a table, you have to start with a function

Answer 33

as you can check, the first function:
y=(1/2)(x+1) passes at point (-1,0)

Answer 34

ok so i would make a table for each function

1. f(x) = x^2 - 1
2. y = x + 1
3. f(x) = 2^x -1

Answer 35

whereas the second function:
y=-x+5, passes at point (2,3)

Answer 36

ok so I would start with the first point each function passes through to the fifth point they pass?

Answer 37

yes! It is a possible procedure

Answer 38

ok so thats all I would do then explain? thanks so much!

Answer 39

:)