# finding the max or min of a quadratic function

label Algebra
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g(x)=-3x²+6x-6

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=

Oct 10th, 2015

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g(x) = -3x²+6x-6

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

$\\ x=\frac{-b}{2a}\\ \\ x=\frac{-6}{2\times(-3)}\\ \\ x=\frac{-6}{-6}\\ \\ x=1$

Substitute x = 1 in g(x) to get the maximum value.

$\\ g(1)=-3\times1^2+6\times1-6\\ \\ g(1)=-3+6-6\\ \\ g(1)=-3$

So the functions maximum value is -3.

The maximum value occurs at x = 1.

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Oct 10th, 2015

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Oct 10th, 2015
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Oct 10th, 2015
Nov 17th, 2017
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