SOLUTION: g(x)=3x^2+12x+9 does this function have a minimum or maximum value what is the function minimum or maximum value where does the minimum or maximum value occur x=

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: g(x)=3x^2+12x+9 does this function have a minimum or maximum value what is the function minimum or maximum value where does the minimum or maximum value occur x=      Log On


   

Question 881498: g(x)=3x^2+12x+9
does this function have a minimum or maximum value
what is the function minimum or maximum value
where does the minimum or maximum value occur
x=
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Have Min? YES because 3%3E0.

Use Completing the Square to put the function into standard form and read the vertex (the minimum point) from the equation. This shows how to Complete the Square.

The function which you have is factorable enough that you can find the roots, and from the roots, find the x value at the vertex, and use this x value (exact mid point of the two roots) to compute the y value for the vertex.

g%28x%29=3%28x%2B1%29%28x%2B3%29, and finding roots:
%28x%2B1%29%28x%2B3%29=0
x=-1 or x=-3.
-
The exact middle of those x-intercepts is -2. This is the line of symmetry of the function and the minimum point of the parabola.
g%28-2%29=3%28-2%2B1%29%28-2%2B3%29
3%28-1%29%281%29
highlight%28g%28-2%29=-3%29, the minimum value, vertex (-2,-3).