SOLUTION: Find the equation of the parabola whose vertex is on the line y=x, axis parallel to x-axis and passing throught (6,-2) and (3,4)

Question 1062373: Find the equation of the parabola whose vertex is on the line y=x, axis parallel to x-axis and passing throught (6,-2) and (3,4)
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
The general form and the two given points should allow you to make a linear system of two equations in three unknown variables. You should be able to eliminate two of them. Your next equation y=x might allow you to find the value for the last unknown variable. Converting from general form into standard form might also help.

The best I have been able to find so far is ,
and the vertex being on line y=x, would be some point ( , ).

The linear equation of a and b, and the expected vertex being on line y=x justify a system . Still not a final answer.

The system most likely to give something meaningful might be the two specific point equations, and the vertex coordinate relationship equation:
.

Solve the first of those for c and substitute into the next two equations. This should be able to make a system
.
Notice that the first equation here has a term , and that a few of the other equation's terms can be factored with
might be useful. This could give a single equation in just the one variable, b.

Do that and you get . Quadratic formula solution will then after simplification give you just for b,
.

Still a ways to go to get the possible "a" and "c" values.
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