SOLUTION: A graph of a parabola has a line of symmetry at x=3 and contains the points (5,-3) and (-1,9). Determine an equation for the parabola.

Question 378095: A graph of a parabola has a line of symmetry at x=3 and contains the points (5,-3) and (-1,9). Determine an equation for the parabola.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The vertex form is . Since the line of symmetry is x = 3, then the x-ccordinate of the vertex is h = 3. Thus the equation now is .
We have to find a and k. Use the coordinates of the given point.
From (5, -3): , or -3 = 4a + k, or k = -4a-3.
From (-1, 9): , or 9 = 16a + k, or k = 9 - 16a.
Hence -4a - 3 = 9 - 16a.
12a = 12, or a = 1.
Then k = -4*1-3 = -7. Therefore the equation of the parabola is
.
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