SOLUTION: Find a quadratic equation f(x) = ax^2+bx+c whose graph has a maximum value at 25 and x-intercepts -3 and 2.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Find a quadratic equation f(x) = ax^2+bx+c whose graph has a maximum value at 25 and x-intercepts -3 and 2.      Log On


   

Question 327596: Find a quadratic equation f(x) = ax^2+bx+c whose graph has a maximum value at 25 and x-intercepts -3 and 2.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=C%28x%2B3%29%28x-2%29
where C is a constant to be determined using the maximum value of 25.
Move from this general form to the vertex form,
f%28x%29%2FC=x%5E2-2x%2B3x-6
f%28x%29%2FC=x%5E2%2Bx-6
f%28x%29%2FC=%28x%5E2%2Bx%2B1%2F4%29-6-1%2F4
f%28x%29%2FC=%28x%2B1%2F2%29%5E2-25%2F4
f%28x%29=C%28x%2B1%2F2%29%5E2-%2825C%29%2F4
The vertex of the equation is (-1/2,-25C/4) and the maximum occurs at the vertex.
For the maximum value equal to 25,
-%2825C%29%2F4=25
C=-4
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f%28x%29=-4x%5E2-4x%2B24
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