SOLUTION: Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.      Log On


   

Question 1039113: Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-h%29%5E2%2Bk standard form with vertex (h,k).

Two of your given points have the same y coordinate for different x coordinates, telling you where the axis of symmetry is:

%28-2%2B4%29%2F2=2%2F2=1 the middle x value of those two points, giving y=a%28x-1%29%5E2%2Bk.

You are given a y-intercept, which may give more information for the equation.
y=a%280-1%29%5E2%2Bk
-4=a%280-1%29%5E2%2Bk
-4=a%2Bk


What you have found currently is this:
system%28y=a%28x-1%29%5E2%2Bk%2Ca%2Bk=-4%29

Either of the other points should give more information.
Use (4,-20),
-20=a%284-1%29%5E2%2Bk
-20=9a%2Bk

Summarize again everything found:
system%28y=a%28x-1%29%5E2%2Bk%2Ca%2Bk=-4%2C9a%2Bk=-20%29
The two equations here with only variables a and k will permit finding values for a and k.
-
a%2Bk-%289a%2Bk%29=-4-%28-20%29
-8a=-4%2B20
8a=4-20=-16
highlight%28a=-2%29
-
a%2Bk=-4
k=-4-a
k=-4-%28-2%29
k=-4%2B2
highlight%28k=-2%29


EQUATION: highlight%28y=-2%28x-1%29%5E2-2%29


graph%28300%2C300%2C-2%2C8%2C-8%2C2%2C-2%28x-1%29%5E2-2%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The general model for quadratic function is:



Given that the point is on the graph of , then the following must hold:



which is to say,



Similarly, considering the other two given points:



which is to say



and



or



Substituting the now known value of and simplifying, we get the following 2X2 system:





Solve the 2X2 system for a and b, which, along with -4 for c can be substituted into to get the desired function.

John

My calculator said it, I believe it, that settles it