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The graph of $y=x^{2}-4 x+4$ is tangent to the $x$ -axis at $x=2$ and does not intersect the$x$ -axis at any other point. How many roots does this function have? Explain your answer.

Two roots (a double root)

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 5

Polynomial Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Missouri State University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

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02:05

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02:25

Find an equation of the ta…

all right. So for this exercise, we are given the function. Why equals X squared minus for X Plus four. And we're told that it is tangent to the X axis of value. X equals two. And the question is, how many roots does this function have? So if we were to factor this polynomial, we see that we can rewrite it as quantity X minus two times the quantity X minus two. And if we foil that out, so x times x x squared X times negative too is negative two x, another negative to X and now a positive force. So you can see that this expression is equivalent to this expression so we can actually rewrite this as X minus two squared. And the question is, how many roots does this polynomial half? Well, this polynomial has only one route, but it occurs twice because there's two occurrences of the negative to through. So what we say is that this has one route with multiplicity to multiplicity means that the number of times that it occurs as a root in the polynomial. So in this case, negative two is the only route. But it has melted

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