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Determine whether the given equations is a circle, a point, or a contradiction (no real graph).$$(x+3)^{2}+(y-2)^{2}=0$$

Point

Algebra

Chapter 1

Functions and their Applications

Section 5

The Circle

Functions

Campbell University

Oregon State University

Harvey Mudd College

Lectures

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In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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for this problem, We're going to examine the equation. X plus three squared. Plus why minus two squared equals zero. And our challenge for this exercise is to determine what the graph of this equation looks like. Is it a circle? Is it a point or is it a contradiction? In other words, perhaps there is no real graph that satisfies this equation. Well, how do we know what case we have? We're going to use the fact that this equation is given to us in standard form. Put this in. Just general standard for standard form is X minus H squared. Plus why minus k squared equals R squared. When we're in standard form, we can use this r squared to tell us which of these three cases we have. If r squared is positive. Any positive number? We have a circle. I just take that number. I take the square root that tells me what my radius is. If r squared equals zero, we have a point. We eggs. The circle exists at that central point, but it doesn't go anywhere. There's no radius, so rate at R squared zero gives me a point. And if r squared is negative, then that's a contradiction. Because no matter what really number value I have for the radius, when I square it, it has to be positive. So a negative square is a contradiction. So let's take a look at the equation we've been given. We're already in standard form and R R squared is zero. That means the second cases. In effect, we have a point. In fact, a point is at the center of our circle, which is going to be negative 32

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