finding the max or min of a quadratic function
Algebra

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answer the questions below about the quadratic function
g(x)=3x²+6x6
a. does the function have a minimum or maximum value
b. what is the function's min or max value
c. where does it occur x=
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g(x) = 3x²+6x6
The general form of a quadratic equation is
g(x) = ax² + bx + c
Comparing the two equations we get
a = 3
b = 6
c = 6
We can decide whether the given quadratic function has a maximum or minimum value by looking at the coefficient of x² which is a.If a < 0 then the parabola opens downward and so the vertex will be the highest point on the curve. So it will have a maximum value.
If a > 0 then the parabola opens upward and so the vertex will be the lowest point on the curve. So it will have a minimum value.
In this case the coefficient of x² is a = 3 < 0.
So the function has a maximum value.
Vertex occurs where
Substitute x = 1 in g(x) to get the maximum value.
So the functions maximum value is 3.
The maximum value occurs at x = 1.

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