SOLUTION: The graph of a function F is a parabola that has the x-intercepts 9 and 21. The function has a minimum value of -54 Thanks

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Question 948148: The graph of a function F is a parabola that has the x-intercepts 9 and 21. The function has a minimum value of -54
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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y=a(x-r)(x-s) if r and s are the x-intercepts. Your equation becomes y=a(x-9)(x-21).

Minimum y=-54 means a%3E0. The vertex minimum will occur for x=%289%2B21%29%2F2=10. Use the vertex (10,-54) in the equation to solve for the value of a.

a=y%2F%28%28x-9%29%28x-21%29%29

a=%28-54%29%2F%28%2810-9%29%2810-21%29%29

a=%28-54%29%2F%28%281%29%28-11%29%29

a=54%2F11

The function is highlight%28F%28x%29=%2854%2F11%29%28x-9%29%28x-21%29%29 or equivalent in the form that you want.