SOLUTION: Find a quadratic model for each set of values. (-1, 1), (1, 1), (3, 9)

Question 556161:
Find a quadratic model for each set of values.

(-1, 1), (1, 1), (3, 9)

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Two points determine a linear function; three points determine a quadratic function.
A quadratic function can be written as
or
In general, you can always substitute the coordinates of each of 3 points to get 3 equations.
For your problem,
(-1,1) ---> --->
(1,1) ---> --->
(3,9) ---> --->
You got a system of equations.
From there, you solve the system for a, b, and c and those coefficients determine your quadratic function.
In your case, symmetrical points (-1, 1), and (1, 1) tell you that the axis of symmetry will be the y-axis (the line x=0), making b=0.
In your case or
The simplest quadratic function (the mother of all quadratic functions) is
or
Without grabbing your pencil (or pen), you can see that it passes through all 3 of your points. There is only one quadratic function that passes through any set of 3 points, so
Your function is or .
(But you can solve the system of equations if it makes you, or your teacher happy. It's an easy one.)
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