Given the following quadratic equation, determine if it has a maximum or a minimum value. Then find the maximum or minimum value.  f(x) = -3x^2 + 6x

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lemjay | High School Teacher | (Level 3) Senior Educator

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Note that the graph of a quadratic function is a parabola. It has a minimum point if the parabola opens up. And a maximum point if it opens down.

When the coefficient of `x^2` is positive, parabola opens up. And if negative, it opens down.

For the given function `f(x)= -3x^2+6x` ,  the coefficient of `x^2` is -3. So, the parabola opens down and it would have a maximum point.

Also, the maximum and minimum point of the parabola is its vertex.

To determine the vertex (h,k) , use the formula:

`h=-b/(2a) `    and  `k=f(h)`

where a is the coefficient of `x^2` and b coefficient of `x` .

`h=-6/(2*(-3)) = -6/(-6)=1`

Substitute x with the value of h to the given function.

`k=f(1)=-3(1)^2+6(1)=-3+6=3`

Hence, the function `f(x)=-3x^2+6x` has a maximum point at (1,3).

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