00:01
So remember, the first thing we want to do when we're trying to sketch a polynomial is figure out the intercepts, as well as their multiplicity.
00:08
So for this polynomial, we have an intercept at x is equal to 0 and at x is equal to positive 5.
00:16
Well, at x is equal to 0, we have a multiplicity of 1.
00:19
So this means it'll cross the x -axis, and at x is equal to 5, this has a multiplicity of 2.
00:26
And so this means this will only touch the x -axis.
00:29
So now let's look at our end behavior here.
00:32
Well, if we have x's, x approaches positive infinity, well, then our polynomial is positive infinity times positive infinity squared.
00:43
So this is, this approach is positive infinity.
00:45
And so when x approaches negative infinity, we have a negative infinity times a negative infinity squared...