I need help on a assignment!

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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!
I need help on 4 and 5
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.

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Other answers:

2 real zeros when b^2 = 4 a c from the general equation ax^2 + bx + c = 0
wait how would i explain it for number 4?
upward opening means a is positive
I did 1-3. I just need some help on 4 and 5
show what you have then
ok hang on one sec
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
@Michele_Laino please help
@triciaal where are you going??
It seems that your answer is right!
thanks! umm im just confused about 4 and 5 though can you help? @Michele_Laino
I think that we have to write the function of each on-ramp
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
yes! I think so!
ok thanks! what about number 5??
how would i make the tables?
for part #5, we have to construct those two on-ramps
how would i do that
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
wait i already did that? number 5 wants a table how do i do that?
I think that one on-ramp can be represented by this function: \[y = \frac{1}{2}\left( {x + 1} \right)\]
i'm confused now?
and the second one, can be represented by this function: \[y = - x + 5\]
for number 5? arent they asking for a table though
I know, nevertheless in order to write a table, you have to start with a function
as you can check, the first function: y=(1/2)(x+1) passes at point (-1,0)
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
whereas the second function: y=-x+5, passes at point (2,3)
ok so I would start with the first point each function passes through to the fifth point they pass?
yes! It is a possible procedure
ok so thats all I would do then explain? thanks so much!
:)

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