SOLUTION: A parabola has an x intercept at 2, its axis symmetry is the line x=4 and the y coordinate of its vertex is 6. Determine the equation of the parabola. How do I begin to solve this?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A parabola has an x intercept at 2, its axis symmetry is the line x=4 and the y coordinate of its vertex is 6. Determine the equation of the parabola. How do I begin to solve this?      Log On


   

Question 978623: A parabola has an x intercept at 2, its axis symmetry is the line x=4 and the y coordinate of its vertex is 6. Determine the equation of the parabola. How do I begin to solve this? There is a hint y-r=a(x-t)^2. Not sure how to use that.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Almost. Use one more term, although shown with different variables:
y=a%28x-h%29%5E2%2Bk.

The vertex is (4,6) which corresponds to (h,k). The given x-intercept is (2,0) and because of symmetry, the other is (6,0). So far you have enough to know y=a%28x-4%29%5E2%2B6.

Solve for a, and then substitute either coordinate values for either x-intercept...