How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y = x^2 +6x + 2#?
Differentiate the expression to find an equation for its slope and set the slope equal to
Line of symmetry:
It is simplest to take the elements of this question in a different order, and this is often a useful tip in answering questions in math and science. The order things are listed in in the question might not be the best order to do them in.
It's start by finding the maximum or minimum, but even before that I'd think about it a bit. Ignore the complexity for the moment, and this equation has
A minimum (or maximum) is a point where the slope is
How to we find the slope of a curve? Using differentiation. The first derivative of a curve is its gradient:
(f you've been assigned this question, you should already know how to differentiate an expression like this!)
Then we can simply set that equal to
The x-coordinate of the minimum is
To find the y-coordinate of the minimum, simply plug this value,
So the minimum is at the point
We know the location of the minimum and the line of symmetry. It might be helpful to know the locations of a few more points to help us graph the function. The x-intercepts and y-intercepts are useful ones. The y-axis is the line
We do the same trick to find the x-intercepts, by setting
This is a quadratic equation, and we can solve it with the quadratic formula or other means.
Those points and understanding the shape of a parabola should be enough to graph the function.