Graphing Circles in Standard Form

This video tutorial explains how to graph a circle given in standard form. It covers identifying the center and radius from the equation, understanding the standard form, and plotting the circle on a graph. The tutorial emphasizes the importance of recognizing the opposite signs in the equation for the center coordinates and calculating the radius from R squared.

What is the standard form equation of a circle?

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r

• x^2 + y^2 = 2r

If the equation has (x - 2)^2, what is the x-coordinate of the center?

• -2

• 0

• 4

• 2

What does the term (y + 3)^2 indicate about the y-coordinate of the center?

• -3

• 3

• 9

• 0

How do you correctly interpret the signs of h and k in the standard form equation?

• As the square of the coefficients

• Opposite of the signs in the equation

• Directly as they appear

• None of the above

What is the radius of a circle if r^2 = 16?

• 8

• 4

• 16

• 2

How do you find the radius from the equation if given r^2?

• Multiply r by 2

• Divide r^2 by 2

• Square r

• Take the square root of r^2

Where is the center of the circle located if the equation is (x - 2)^2 + (y + 3)^2 = 16?

• (2, 3)

• (-2, -3)

• (-2, 3)

• (2, -3)

How many units do you move from the center to sketch the circle if the radius is 4?

• 2 units

• 4 units

• 16 units

• 8 units

What is the correct method to find points on the circle for graphing?

• Only move horizontally from the center

• Only move vertically from the center

• Move horizontally and vertically from the center

• Move diagonally from the center

What ensures that every point on the circle is the correct distance from the center?

• Each point is half the radius distance

• Random placement of points

• Each point is twice the radius distance

• Each point is at the radius distance