SOLUTION: find the particular quadratic equation in standard form, of the parabola with vertex at (2,-5) and passing through (3,1). You know the third point because of symmetry. What are the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: find the particular quadratic equation in standard form, of the parabola with vertex at (2,-5) and passing through (3,1). You know the third point because of symmetry. What are the      Log On


   

Question 1112770: find the particular quadratic equation in standard form, of the parabola with vertex at (2,-5) and passing through (3,1). You know the third point because of symmetry. What are the x and y intercepts?
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by solver91311(24713) About Me  (Show Source):
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You are given sufficient information to write the function in vertex form directly except for the lead coefficient.



where and are the coordinates of the vertex. Hence:


(pay careful attention to the signs on the vertex coordinates)

We also know that:



Hence



So



Giving



Which expands and simplifies to:



The quadratic formula provides the -intercepts.

Alternatively:

We are given and and we know by symmetry that

So since the general standard quadratic function is

We can write



and



or more simply:







The best and least error-prone method of solving this system is by Gauss-Jordan Row Reduction. I will leave that as an exercise for the student. Performed correctly the process will yield the same coefficients as the method shown above.
Again, the -intercepts are obtained with the quadratic formula.

John

My calculator said it, I believe it, that settles it