Question 709087: The zeros of a quadratic relation are 0 and 6. The relation has a minimum value of -9. Find the equation of the parabola.
Please include steps so I can understand the solution to the answer. Thanks in advance.
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Assuming this parabola has a vertical axis, we can find the other coordinate of the minimum. Zeros at x=0 and x=6 mean that the symmetry axis runs directly in the middle, at x=3. Vertex (the minimum point in this case) is at (3,-9).
You now have something which in standard form can be written as
 , which has only one undetermined value, "a". The x and y are variables but would ordinarily remain as variables. You can still use the given points (0,0) and (6,0) to help find the still unknown "a".
Known points for this graph: (0,0), (6,0), (3,-9).
The rest of the description of this solution is still left unfinished, but maybe you can decide what to do the rest of the way.
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