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