SOLUTION: Find a quadratic model for the set of values: (-2, -20), (0, -4), (4, -20). Show your work.
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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(39620) (Show Source): You can put this solution on YOUR website!
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:
the middle x value of those two points, giving .
You are given a y-intercept, which may give more information for the equation.
What you have found currently is this:
Either of the other points should give more information.
Use (4,-20),
Summarize again everything found:
The two equations here with only variables a and k will permit finding values for a and k.
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-
EQUATION:
Answer by solver91311(24713) (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:
^2\ +\ b(-2)\ +\ c\ =\ -20)
which is to say,
Similarly, considering the other two given points:
^2\ +\ b(0)\ +\ c\ =\ -4)
which is to say
and
^2\ +\ b(4)\ +\ c\ =\ -20)
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
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