SOLUTION: What is the equation of a parabola with vertex on the line y=x, axis parallel to Ox, and passing through (6,-2) and (3,4)?

Question 1045379: What is the equation of a parabola with vertex on the line y=x, axis parallel to Ox, and passing through (6,-2) and (3,4)?
Found 2 solutions by KMST, advanced_Learner:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let the vertex be .
The equation of a parabola with that vertex and axis parallel to the x-axis is
.
Substituting the coordinates of the given points, we have
--->
--->
Those two equations form a system of equation we have to solve to find and .
Subtracting one equation from the other, we have

Substituting the expression for in we get
-->-->
-->
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The solutions to that equation are and .
Only one of those solutions should work, because
through any 3 points, (such as (6,-2) , (3,4), and )
passes only one parabola with axis parallel to the x-axis.
Substituting for in the original equation
, we get
--->--->
The values also satisfy equation .
So, is the equation of a parabola with vertex on the line , axis parallel to the x-axis, and passing through (6,-2) and (3,4).
The equation can be written in other, equivalent forms.
<--><-->

NOTE: The solution does not yield the same a value when substituted in the two original equations.
Answer by advanced_Learner(501) (Show Source): You can put this solution on YOUR website!
.

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