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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

1. Equations and Inequalities

The Square Root Property

1. Equations and Inequalities

The Square Root Property: Videos & Practice Problems

Video Lessons Practice Worksheet

19 problems

Problem 1Multiple Choice

Among the following equations, select which one can be directly solved by using the quadratic formula and work out the value(s) of x.

1. 4x² - 23x - 35 = 0
2. (3x + 1)² = 4
3. x² - x = 72
4. (9x - 4)(x - 5) = 0

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Problem 2Multiple Choice

Among the following equations, select which one can solved by skipping the first step in completing the square and work out the value(s) of x.

1. 4x² - 23x - 35 = 0
2. (3x + 1)² = 4
3. x² - x = 72
4. (9x - 4)(x - 5) = 0

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Problem 3Multiple Choice

Use the zero-factor rule to solve the given quadratic equation.

-8x² + 17x = -21

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Problem 4Multiple Choice

In the given equation, complete the square and solve it.
18x² +x = 4

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Problem 5Multiple Choice

In the given equation, complete the square and solve it.
4x² - 24x +111= 0

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Problem 6Multiple Choice

For the following equation, express y in terms of x:

9x² - 15xy + 5y² = 7

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Problem 7Multiple Choice

Identify the number of distinct solutions of the following quadratic equation by calculating its discriminant. Then, classify the solutions (nonreal complex number, rational, or irrational):

12x² - 5x + 2 = 0

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Problem 8Multiple Choice

Solve the quadratic equation given below for x.

(x + 3)(x + 6) = 3x

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Problem 9Multiple Choice

Identify the following function's graph by first solving for its x-intercepts and then matching it with the given graphs.

y = 2x² -8x +9

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Problem 10Multiple Choice

Solve the equation x^2 = 49 using the square root property.

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Problem 11Multiple Choice

What is the first step in solving the equation 3x^2 - 12 = 0 using the square root property?

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Problem 12Multiple Choice

Solve the equation x^2 = 20 and simplify your answer.

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Problem 13Multiple Choice

Solve the equation x^2 + 16 = 0.

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Problem 14Multiple Choice

Which of the following equations is most suitable for solving using the square root property?

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Problem 15Multiple Choice

If x = ±3 is a solution to the equation x^2 = 9, verify the solution by substitution.

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Problem 16Multiple Choice

What type of solutions does the equation x^2 = -4 have?

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Problem 17Multiple Choice

Predict the type of roots for the equation 2x^2 + 3 = 0.

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Problem 18Multiple Choice

Solve the equation (x - 3)^2 = 25 by breaking down the steps.

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Problem 19Multiple Choice

Why is it important to consider both the positive and negative square roots when solving x^2 = k?

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Intro to Quadratic Equations Practice Problems Completing the Square Practice Problems

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The Square Root Property: Videos & Practice Problems

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