Circle Equations: Completing the Square Techniques

This video tutorial covers the process of completing the square to solve quadratic equations and apply this technique to find the equation of a circle. It begins with a review of the steps involved in completing the square, followed by a detailed walkthrough of solving a quadratic equation. The tutorial then explores the applications of this method, particularly in converting the general form of a circle's equation to its center-radius form. By the end, viewers will understand how to use completing the square as a tool for solving quadratics and writing circle equations.

What is the main goal of this video?

• To solve linear equations

• To find the equation of a circle using completing the square

• To understand the quadratic formula

• To learn how to factorize polynomials

What is the first step in completing the square?

• Add a perfect square to both sides

• Square the constant term

• Divide by the coefficient of x

• Move the constant to the other side

Why do we divide by the coefficient of x squared in completing the square?

• To eliminate the constant term

• To simplify the equation

• To make the coefficient of x squared equal to 1

• To factorize the equation

How do you find the value to add to both sides to complete the square?

• Divide the coefficient of x by 2 and square it

• Multiply the coefficient of x by 2

• Square the constant term

• Add the coefficient of x to the constant term

What is the result of adding 1/16 to both sides of the equation?

• An exponential equation

• A quadratic equation

• A perfect square trinomial

• A linear equation

What are the four methods to solve quadratic equations mentioned in the video?

• Factoring, graphing, substitution, and elimination

• Graphing, substitution, elimination, and completing the square

• Factoring, substitution, elimination, and quadratic formula

• Factoring, graphing, completing the square, and quadratic formula

What does solving a quadratic equation mean?

• Finding the minimum value

• Finding the roots or x-intercepts

• Finding the y-intercepts

• Finding the maximum value

What is the first step in converting the general form of a circle's equation to the center-radius form?

• Add a perfect square to both sides

• Divide by the coefficient of x squared

• Group the x and y terms

• Move the constants to the other side

How do you balance the equation after adding the perfect squares?

• Divide both sides by the same value

• Subtract the same values from both sides

• Add the same values to the other side

• Multiply both sides by the same value

What is the center of the circle in the final equation?

• (0, 0)

• (2, 3)

• (3, 2)

• (1, 1)