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, a = 1 and b = -2, so...
This is the x-coordinate of the vertex.
To find the y-coordinate, substitute x = 1 into the given quadratic equation and solve for y:
Substitute x = 1.
The vertex (or the minimum in this case) is at (1, -9)
Let's see what the graph looks like:
(