SOLUTION: Please help me solve this equation in standard form of the parabola passing through the points: (1,-2), (2,-4), (3,-4)

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Question 792126: Please help me solve this equation in standard form of the parabola passing through the points: (1,-2), (2,-4), (3,-4)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The two points with y=-4 should tell you something about the vertex and symmetry axis. The other point will let you find the coefficient .

The points (2,-4) and (3,-4) tell you that the axis of symmetry and the x value for the vertex is at 5%2F2=2%261%2F2.

Make this system of equations, using GENERAL FORM:
y=ax%5E2%2Bbx%2Bc in which a, b, and c are the unknowns.
a%2A1%5E2%2Bb%2A1%2Bc=-2.
a%2A2%5E2%2Bb%2A2%2Bc=-4.
a%2A3%5E2%2Bb%2A3%2Bc=-4.
That becomes
a%2Bb%2Bc=-2.
4a%2B2b%2Bc=-4.
9a%2B3b%2Bc=-4.

I resort to an online matrix row-reduction calculator:
a=0.1667, b=-0.8333, c=-3
Which makes seem to be a=1%2F6, b=-5%2F6, c=-3.
General Form for this parabola is highlight%28y=%281%2F6%29x%5E2-%285%2F6%29x-3%29.
Next, you could Complete-the-Square to put this into Standard Form. ALTHOUGH, remember above, where you were able to find that x=5/2 would give the vertex value for y? Use this now! You will then have your (h,k) vertex point which you can fit into your standard form equation. You can probably avoid Completing the Square because you will know vertex, (h,k) and you now know "a" is (1/6), so you have all you need to fill in the standard:
y=a%28x-h%29%5E2%2Bk