Completing the Square and Circle Equations

Completing the Square and Circle Equations

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

Dr. Roger explains how to solve a problem from the May 2021 US SAT about the equation of a circle. He describes the standard form of a circle's equation and demonstrates how to complete the square to find the circle's center and radius. The video concludes with the calculation of the radius and offers tips for SAT preparation, emphasizing the importance of memorizing the circle equation and practicing completing the square.

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main topic discussed in the video?

Finding the area of a triangle

Graphing linear equations

Solving quadratic equations

Understanding the equation of a circle

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the standard form of a circle's equation?

x^2 + y^2 = r^2

x^2 + y^2 = 2r

(x + h)^2 + (y + k)^2 = r^2

(x - h)^2 + (y - k)^2 = r^2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in completing the square for the x terms?

Add 8 to both sides

Subtract 8 from both sides

Take half of the x coefficient and square it

Multiply the x coefficient by 2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What value is added to both sides when completing the square for x?

4

32

16

8

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the next step after completing the square for the x terms?

Solve for y

Complete the square for the y terms

Factor the equation

Calculate the radius

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What value is added to both sides when completing the square for y?

25

5

20

10

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of factoring the completed square for x?

(x - 5)^2

(x + 4)^2

(x + 5)^2

(x - 4)^2

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