Question 244641: Hi! I was wondering if anyone could walk me through how to do this problem?
Write a quadratic function given the following:
(-1,6), (1,4), (2,9)
y=
Thanks!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write a quadratic function given the following:
(-1,6), (1,4), (2,9)
:
Using the form; ax^2 + bx + c = y; we will write three equations:
eq1: x=-1; y=6, substitute for x and y
-1^2a + -1b + c = 6
1a - 1b + c = 6
or just
a - b + c = 6
:
eq2: x=1; y=4
1^2a + 1b + c = 4
a + b + c = 4
:
eq3: x=2, y=9
2^2a + 2b + c = 9
4a + 2b + c = 9
:
We will solve these equations by elimination
Subtract eq 1 from eq 2, eliminate a and c
a + b + c = 4
a - b + c = 6
-----------------subtraction eliminate a and c
0 +2b + 0 = -2
b = -1
:
Substitute -1 for b in the 1st equation
a - (-1) + c = 6
a + 1 = c = 6
a + c = 6 - 1
a + c = 5
:
do the same in the 3rd equation
4a + 2(-1) + c = 9
4a - 2 + c = 9
4a + c = 9 + 2
4a + c = 11
:
Using these two equations:
4a + c = 11
a + c = 5
-------------Subtraction eliminates c, find a
3a = 6
a = 2
:
Find c using a + c = 5
2 + c = 5
c = 5 - 2
c = 3
:
Our equation: y = 2x^2 - x + 3
:
You can check our solution, substitute for x and ensure that it equals y for each given coordinate
:
Did you understand what we did here? Any questions?
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