my question is x=-5, of multiplicity 2. i have to draw it on the graph but i don't know what it means

Question

What does it mean that x=5 is of multiplicity 2? how do i begin this question and what are the steps to answering this question? I do not know where to start and I have other questions like this one.

Answer 1

What this means is that the equation has two solutions, each the same.

 

x = 5, and x = 5, so the equation is y = (x - 5)(x - 5) = (x - 5)².

 

So, the domain is (-∞, ∞) or all real numbers and the range is [0, ∞), or y≥0.

 

The graph is a parabola resting on the point (5, 0) and opening upward with the y-intercept (0, 25).

 

I hope this helps.

Answer 2

Is x=5 or x=-5?

 

Anyway let's say that x=5.  If you have a function say, f(x) = (x-5), this function equals zero when x=5, or, 

f(x) = (x-5) = 0 when x=5.  Now, consider the function g(x) = (x-5)^2 or equivalently, g(x)=(x-5)(x-5) which equals zero when x=5.  Since there are two instances of (x-5) we say that x=5 is a root of multiplicity 2.  So your graph would be that of g(x) = (x-5)^2