Question

Identify the center and radius of each. Then sketch the graph.

Answer 1

Answer:

Step-by-step explanation:

Can't sketch it, obviously, but I can help you understand how to do that on your own. The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$ where h and k are the coordinates for the center of the circle. The super-important thing to remember here is that the standard form is ALWAYS (x-h)^2 (the minus being the important part!). That means that if the expression is

$(x-2)^2$ for example, it can be rewritten to be understood as

$(x-(+2))^2$ where the positive implies movement to the right. If the expression is

$(x+2)^2$ for example, it can be rewritten to be understood as

$(x-(-2))^2$ where negative is indicative of movement to the right. The location of the center of a circle will help you graph it.

In our circle, we have a -1 in with the x and a +3 in with the y. The -1 indicates movement to the right 1 unit (positive 1), while the +3 in with the y indicates movement to the left 3 units (-3).  Therefore, the movement of the circle also indicates the coordinates of the center: (1, -3).

The radius is found in the square root of the number to the right of the equals sign. Ours is a 4; therefore, the radius is 2.

To draw this circle, locate the point (1, -3) on your graph paper and put a dot. Then count directly to the right 2 units and make a dot, directly to the left 2 units and make a dot, directly up 2 units and make a dot, and directly down 2 units and make a dot. Connect the outer 4 dots in as smoothly as possible to get a circle. And there you go!