SOLUTION: How would I find the equation of a parabola whose vertex is (0,0) and two other points are (1,-2) and (-1,-2)?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How would I find the equation of a parabola whose vertex is (0,0) and two other points are (1,-2) and (-1,-2)?      Log On


   

Question 1106268: How would I find the equation of a parabola whose vertex is (0,0) and two other points are (1,-2) and (-1,-2)?
Found 2 solutions by josgarithmetic, math_helper:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This equation should fit y=ax^2, and a<0. Use either given point to find a.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

The vertex form of a parabola is +y+=+a%28x-h%29%5E2+-+k+ where (h,k) = coordinates of the vertex
The vertex is given to be at (0,0), simplifying the above to +y+=+ax%5E2+
Picking one of the other two points (1,-2) allows us to find a:
++-2+=+a%2A%281%29%5E2+
+a+=+-2+ —> +highlight%28y+=+-2x%5E2+%29+
Since a<0, the parabola opens downward