SOLUTION: Find the quadratic function that includes the following sets? (0,6) (2,14), (4,-2)

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Question 1002510: Find the quadratic function that includes the following sets? (0,6) (2,14), (4,-2)
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ax%5E2%2Bbx%2Bc=y
-
system%28a%2A0%2Bb%2A0%2Bc=6%2Ca%2A4%2Bb%2A2%2Bc=14%2Ca%2A16%2Bb%2A4%2Bc=-2%29

system%28highlight%28c=6%29%2C4a%2B2b%2Bc=14%2C16a%2B4b%2Bc=-2%29

system%284a%2B2b%2B6=14%2C16a%2B4b%2B6=-2%29

system%284a%2B2b=8%2C16a%2B4b=-8%29

system%282a%2Bb=4%2C4a%2Bb=-2%29--------R

%284a%2Bb%29-%282a%2Bb%29=-2-4

2a=-6

highlight%28a=-3%29

Return to R,
b=4-2a
b=4-2%28-3%29
highlight%28b=10%29

Put the coefficient found into the general form equation shown at top of this solution posting.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
ax^2+bx+c=0
c=6, using the first point.
4a+2b+6=14
4a+2b=8
2a+b=4
16a+4b+6=-2
16a+4b=-8
4a+b=-2
-2a-b=-4, negating the first
2a=-6, adding
a=-3
b=10
-3x^2+10x+6=0
graph%28300%2C200%2C-10%2C10%2C-10%2C20%2C-3x%5E2%2B10x%2B6%29