SOLUTION: Find the minimum value of x^2-2x-8, if it has one.

Question 992634: Find the minimum value of x^2-2x-8, if it has one.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Does the graph of: have a maximumum and minimum?
Well, it may have a maximum or it may have a minimum, but it doesn't have both!
The graph of a quadratic equation (), such as this, is called a "parabola" and a parabola has a maximum or a minimum depending upon whether it opens upwards (has a minimum) or opens downwards (has a maximum).
You can tell which way the parabola opens by inspecting the coefficient of the term, which is +1 in your problem.
If this coefficient is positive, then the parabola opens upwards and the graph has a minimum.
If the coefficient is negative,then the parabola opens downwards and the graph has a maximum.
The maximum/minimum point (also known as the "vertex") can be found as follows:
The x-coordinate of this point is:
The a is the coefficient of the term and the b is the coefficient of the term.

In your equation, and , so

This is the x-coordinate of the vertex.
To find the y-coordinate, substitute into the given quadratic equation and solve for :
Substitute .

The vertex (or the in this case) is at (, )
Let's see what the graph looks like:

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