How do you complete the square for the equation $$x^2 - 10x + 25 = 36$$ ?

To complete the square, rewrite it as $$(x - 5)^2 = 36$$ .

What is the significance of the discriminant in the quadratic formula?

The discriminant, $$b^2 - 4ac$$ , determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

How do you solve the equation $$4m^2 + 10 = 38$$ by completing the square?

First, rearrange to $$4m^2 = 28$$ , then divide by 4 to get $$m^2 = 7$$ , and finally take the square root to find $$m = \pm \sqrt{7}$$ .

What is the vertex form of a quadratic equation?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

What is the relationship between the coefficients of a quadratic equation and its graph?

The coefficients determine the shape, direction, and position of the parabola on the graph.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is the vertical line that divides the parabola into two mirror-image halves, given by $$x = -\frac{b}{2a}$$ .

How can you check your solution after completing the square?

You can check your solution by substituting the found values back into the original equation to verify equality.

What is the importance of understanding completing the square in algebra?

Completing the square is essential for solving quadratic equations, graphing parabolas, and understanding the properties of quadratic functions.

What is a common mistake when completing the square?

A common mistake is failing to correctly add or subtract the squared term when moving terms around in the equation.

Solve by completing the square Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form of a perfect square trinomial, allowing for easier solutions.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is a perfect square trinomial?

Back

Tags

CCSS.HSA.APR.C.4

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the first step in completing the square for a quadratic equation?

Back

The first step is to move the constant term to the other side of the equation.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What do you do after moving the constant term when completing the square?

Back

Next, take half of the coefficient of the linear term, square it, and add it to both sides of the equation.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

How do you derive the quadratic formula from completing the square?

Back

Start with the standard form of a quadratic equation, move the constant to the other side, complete the square, and solve for x.

Tags

CCSS.HSA-REI.B.4B

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

9 questions

Image and the City. Vocabulary. CPE Practice tests.

Flashcard

•

11th Grade

15 questions

paměť + pozornost

Flashcard

•

9th - 12th Grade

8 questions

Tablet Parts

Flashcard

•

KG

10 questions

Technology vocabulary

Flashcard

•

University

15 questions

Relative Clauses

Flashcard

•

12th Grade

7 questions

International Yoga Day Quiz

Flashcard

•

KG - University

9 questions

Classical and Medieval Art

Flashcard

•

KG

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

54 questions

Analyzing Line Graphs & Tables

Quiz

•

4th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

20 questions

Classifying Polynomials by Degree and Number of Terms

Quiz

•

11th Grade

17 questions

Explore Experimental and Theoretical Probability

Quiz

•

7th - 12th Grade

15 questions

Parallelogram Properties

Quiz

•

10th - 12th Grade

10 questions

Special Right Triangles

Quiz

•

11th Grade

18 questions

Solving Systems- Word Problems

Quiz

•

9th - 12th Grade

34 questions

7.4 Review Cubic and Cube Root Functions

Quiz

•

10th - 12th Grade