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

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) (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 .

Make this system of equations, using GENERAL FORM:
in which a, b, and c are the unknowns.
.
.
.
That becomes
.
.
.

I resort to an online matrix row-reduction calculator:
a=0.1667, b=-0.8333, c=-3
Which makes seem to be , , .
General Form for this parabola is .
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:

RELATED QUESTIONS
1. Find an equation in standard form of the parabola passing through the points. Show... (answered by Alan3354)

Find an equation in standard form of the parabola passing through the points. (1, -1),... (answered by Edwin McCravy)

Find the equation of a line passing through points (-2, 4) and (-1, 6). Put the equation... (answered by josgarithmetic)

Please help me solve this equation: Write the equation of the line passing through... (answered by checkley77)

Find the equation in standard form of the parabola passing through the points below.... (answered by solver91311)

Find an equation in standard form of the parabola passing through the following points.... (answered by lwsshak3)

Find the equation in standard form of the parabola passing through these points (1,7)... (answered by solver91311)

find the equation in standard form for the parabola passing through the points (2,-8)... (answered by lwsshak3)

Please help me solve this equation: Write the equation of the line passing through... (answered by nerdybill)