Question

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.

Answer 1

will reward medal
and fan

Answer 2

@PlsHaveMercyLilB
@BlackLabel

Answer 3

x^2-1 looks like this

Answer 4

as you can see, there are 2 real zeros

Answer 5

setting x^2-1 = 0 will give you two real zeros

Answer 6

thank you

Answer 7

that should be proof enough, you might have to include that a zero occurs when f(x) = 0

Answer 8

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.

Answer 9

@PlsHaveMercyLilB

Answer 10

@PlsHaveMercyLilB

Answer 11

So you can just decide where on the freeway you want the ramps? any place?

Answer 12

yes

Answer 13

just pick any 2 points (x, f(x)).... its not that hard just try it

pick two x-values
I chose x=2 and x=3
now find f(2) and f(3)
f(x)= x^2-1
f(2) = 2^2 -1 = 3
f(3) = 3^2 -1 = 8
so, two points on this function are (2, 3) and (3, 8) which are two points that you can have a ramp at

Answer 14

this is the rubric 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.

coordinate plane showing quadratic functions f of x with zeros labeled and two additional points labeled as on ramps. Linear function h of x passes through both on ramp points. Exponential function j of x passes through one on ramp pointcoordinate plane showing quadratic functions f of x and g of x, with zeros labeled and four additional points labeled as on ramps. Linear function h of x passes through two on ramp points on function f of x. Exponential function j of x passes through one on ramp point on g of x
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.

If you are doing this project collaboratively, then your partner will need to create a unique second freeway function, g(x), and prove that it also has two real zeros.

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.

If you are working collaboratively, identify four on-ramps, two on each function.

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.

Collaborative pairs need to connect linear function h(x) through the on ramp points on f(x), and connect exponential function j(x) through any on ramp point on g(x). At least three of the four on ramp points will be used.

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.

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.

Collaborative groups should prove whether f(x) or h(x) is the most northern between the two, and whether g(x) or j(x) is the most northern between those two.
Include your graph that shows the functions that model each of the roads and the on-ramps.

Answer 15

bruh i got my own homework

Answer 16

haha

Answer 17

btw im doin flvs too lol

Answer 18

what math

Answer 19

ap calc bc its the highest one so kinda hard lol

Answer 20

oh