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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

Oregon State University

Harvey Mudd College

Idaho State University

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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Determine whether the give…

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Determine whether the grap…

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Solve the given problems.<…

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for this problem. We're going to examine the equation. X minus three squared. Plus why plus two squared equals zero. And the goal for this problem 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, is there no riel graph that matches up with this equation? Well, how do we know what this equation looks like? We're going to take advantage of the fact that this is in that standard form. Standard form for a circle is X minus H squared. Plus why minus k squared equals R squared H and K. That's the central point of our circle. But we're going to look at the R squared. We're going to take advantage of that number to tell us what this graph is gonna look like. If R squared is greater than zero than we have a circle, any positive number, I could take the square root, and that's my radius. That gives me a circle. If r squared equals zero, then we have a point. My circle exists at that center point, and it doesn't go anywhere, so my I'm reduced to a single point, and if our square is negative, then that's a contradiction. It doesn't matter what radius I give a circle. If I take a number and square, it has to give me a positive number and negative squared number. That's a contradiction. It means there's no real graph that goes along with my equation. So let's take a look at what we've been given. We have it, this equation in standard form, and it is equal to zero. Well, that's my second condition here. That means I have a point. In fact, the point is at my central point, which is the 0.0.0.3 negative, too.

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