SOLUTION: Find the quadratic function {{{f(x)=ax^2+bx+c}}} for which f(1)=6 , f(-2)=18 , and f(2)=6. I need help with this one. I am having a hard time figuring it out!

Question 675648: Find the quadratic function for which f(1)=6 , f(-2)=18 , and f(2)=6. I need help with this one. I am having a hard time figuring it out!
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the quadratic function for which
You have 3 points. Substitute into the quadratic form and solve the system:
----------------------------------
f(1)=6 ::: a + b + c = 6
f(-2)=18::4a -2b + c = 18
f(2)=6::::4a +2b + c = 6
-------
I used a matrix method on a TI-84 to get:
a = 1
b = -3
c = 1
==========
Equation:
y = x^2 -3x + 1
====================
Cheers,
Stan H.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

for f(1)=6

..............1
f(-2)=18

..............2
and f(2)=6

.................3
solve this system:
..............1
..............2
.................3
______________________________
..............1...solve for
........substitute in 2

..............2

....both sides divide by
.....solve for

..........substitute in

substitute and in 3

.................3
.....solve for

now find

and

so. your function is:

let's see if all given points lie on this parabola

points are:f(1)=6 , f(-2)=18 , and f(2)=6, or (1,6),(2,6),(-2,18)

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