How do you solve $$ (x - 7)^2 = 99 $$ using the Square Root Property?

Take the square root of both sides: $$ x - 7 = \text{±} \\sqrt{99} $$ . Then, solve for x: $$ x = 7 \text{±} 3\\sqrt{11} $$ .

What are the solutions to $$ x^2 = 49 $$ ?

The solutions are $$ x = 7 $$ and $$ x = -7 $$ .

How do you solve $$ 2(2x - 4)^2 = 32 $$ ?

First, divide both sides by 2: $$ (2x - 4)^2 = 16 $$ . Then, take the square root: $$ 2x - 4 = \text{±} 4 $$ . Solve for x to get $$ x = 0 $$ and $$ x = 4 $$ .

What is the solution to $$ 3 + 9r^2 = 12 $$ ?

Subtract 3 from both sides: $$ 9r^2 = 9 $$ . Divide by 9: $$ r^2 = 1 $$ . Take the square root: $$ r = 1 $$ and $$ r = -1 $$ .

How do you solve $$ x^2 + 12 = 5 $$ ?

Subtract 12 from both sides: $$ x^2 = -7 $$ . Since the square of a real number cannot be negative, the solutions are $$ x = \text{±} i \\sqrt{7} $$ .

What does it mean if a quadratic equation has no real solutions?

It means that the expression under the square root (the discriminant) is negative.

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root: $$ b^2 - 4ac $$ . It determines the nature of the roots.

What is the general form of a quadratic equation?

The general form is $$ ax^2 + bx + c = 0 $$ , where a, b, and c are constants and @@ a eq 0 @@.

How can you check your solutions after solving a quadratic equation?

Substitute the solutions back into the original equation to verify if both sides are equal.

What is the significance of the Square Root Property in solving quadratic equations?

It allows for a straightforward method to find solutions when the equation is in the form of a perfect square.

What is a perfect square trinomial?

A perfect square trinomial is an expression of the form $$ (a + b)^2 = a^2 + 2ab + b^2 $$ or $$ (a - b)^2 = a^2 - 2ab + b^2 $$ .

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

The roots of a quadratic equation correspond to the x-intercepts of its graph, where the parabola intersects the x-axis.

What is the vertex of a parabola?

The vertex is the highest or lowest point of the parabola, depending on its orientation, and can be found using the formula $$ x = -\frac{b}{2a} $$ .

Solving Quadratic Equations using the Square Root Property Flashcard

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Square Root Property?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

7.

FLASHCARD QUESTION

Front

What is the first step in solving a quadratic equation using the Square Root Property?

Back

Isolate the squared term on one side of the equation.

Tags

CCSS.HSA-REI.B.4B

Create a free account and access millions of resources

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

By signing up, you agree to our Terms of Service & Privacy Policy

Already have an account?

Similar Resources on Wayground

10 questions

2025 S3/4 CCKS Enzymes

Flashcard

•

8th Grade - University

11 questions

Unit 1 | Topic 2 | Key Terms - Flashcards

Flashcard

•

9th - 12th Grade

15 questions

Unit 4 Test Review

Flashcard

•

10th Grade - University

11 questions

Genetic Engineering Concepts

Flashcard

•

11th Grade - University

8 questions

MAT_8_EF_QN01-QN08

Flashcard

•

8th Grade - University

10 questions

Disney descendants flashcard

Flashcard

•

KG

15 questions

Function Operations and Composite Functions

Flashcard

•

9th Grade - University

Popular Resources on Wayground

10 questions

Honoring the Significance of Veterans Day

Interactive video

•

6th - 10th Grade

10 questions

Exploring Veterans Day: Facts and Celebrations for Kids

Interactive video

•

6th - 10th Grade

19 questions

Veterans Day

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

15 questions

Circuits, Light Energy, and Forces

Quiz

•

5th Grade

6 questions

FOREST Self-Discipline

Lesson

•

1st - 5th Grade

7 questions

Veteran's Day

Interactive video

•

3rd Grade

20 questions

Weekly Prefix check #2

Quiz

•

4th - 7th Grade

Discover more resources for Mathematics

15 questions

Two Step Equations

Quiz

•

9th Grade

19 questions

Explore Triangle Congruence and Proofs

Quiz

•

9th - 12th Grade

10 questions

Types of Slope

Quiz

•

6th - 9th Grade

10 questions

Exploring the Basics of Ratios

Interactive video

•

6th - 10th Grade

15 questions

Identify Triangle Congruence Criteria

Quiz

•

9th - 12th Grade

23 questions

Similar Figures

Quiz

•

9th - 12th Grade

16 questions

Domain and Range of Functions

Quiz

•

9th Grade

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade