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1. Review of Real Numbers(0)

Simplifying Fractions
(0)

Evaluating Exponents
(0)

Evaluating Expressions
(0)

Translating Phrases to Expressions
(0)

Translating Sentences to Equations
(0)

The Distributive Property
(0)

Simplifying Expressions
(0)

2. Linear Equations and Inequalities(0)

The Addition and Subtraction Properties of Equality
(0)

The Multiplication and Division Properties of Equality
(0)

Solving Linear Equations
(0)

Linear Inequalities in One Variable
(0)

3. Solving Word Problems(0)

Introduction to Problem Solving
(0)

Formulas
(0)

Percent Problem Solving
(0)

Mixture Problem Solving
(0)

4. Graphing Linear Equations in Two Variables(0)

The Rectangular Coordinate System
(0)

Graph Linear Equations in Two Variables
(0)

Graph Linear Equations Using Intercepts
(0)

Slope of a Line
(0)

Slope-Intercept Form
(0)

Point Slope Form
(0)

5. Systems of Linear Equations(0)

Solving Systems of Linear Equations by Graphing
(0)

Solving Systems of Linear Equations by Substitution
(0)

Solving Systems of Linear Equations by Elimination
(0)

6. Exponents and Polynomials(0)

The Product Rule
(0)

The Quotient Rule
(0)

Intro to the Power Rules
(0)

The Power of a Quotient Rule
(0)

Negative Exponents
(0)

Simplifying Exponential Expressions Using All Exponent Rules
(0)

Intro to Polynomials
(0)

Adding and Subtracting Polynomials
(0)

Multiplying Polynomials
(0)

Special Products
(0)

7. Factoring(0)

Factoring by Greatest Common Factor & Grouping
(0)

Factoring Trinomials of the Form x² + bx + c
(0)

Factoring Trinomials of the Form ax² + bx + c
(0)

Factoring Special Products
(0)

Quadratic Equations & Applications
(0)

8. Rational Expressions and Equations(0)

Simplifying Rational Expressions
(0)

Multiplying and Dividing Rational Expressions
(0)

Adding and Subtracting Rational Expressions with Common Denominators
(0)

Least Common Denominators
(0)

Adding and Subtracting Rational Expressions with Different Denominators
(0)

Rational Equations
(0)

9. Inequalities and Absolute Value(0)

Set Operations and Compound Inequalities
(0)

Absolute Value Equations
(0)

Absolute Value Inequalities
(0)

Linear Inequalities in Two Variables
(0)

Systems of Linear Inequalities
(0)

10. Relations and Functions(0)

Introduction to Relations and Functions
(0)

Function Notation
(0)

Graphing Common Functions
(0)

Composition of Functions
(0)

Direct & Inverse Variation
(0)

11. Roots, Radicals, and Complex Numbers(0)

Introduction to Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Adding and Subtracting Radicals
(0)

Multiplying, Dividing, and Rationalizing Radicals
(0)

Introduction to Complex Numbers
(0)

Multiplying and Dividing Complex Numbers
(0)

12. Quadratic Equations and Functions(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Graphing Quadratic Equations
(0)

13. Inverse, Exponential, & Logarithmic Functions(0)

Introduction to Inverse Functions
(0)

Exponential Functions
(0)

Introduction to Logarithmic Functions
(0)

Properties of Logarithms
(0)

14. Conic Sections & Systems of Nonlinear Equations(0)

Graphing Circles
(0)

Ellipses
(0)

Parabolas
(0)

Hyperbolas
(0)

15. Sequences, Series, and the Binomial Theorem(0)

Introduction to Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

Factorials
(0)

12. Quadratic Equations and Functions

The Quadratic Formula

12. Quadratic Equations and Functions

The Quadratic Formula: Videos & Practice Problems

Video Lessons Practice Worksheet

25 problems

Problem 1Multiple Choice

Given the quadratic equation $3 x^{2} - 7 x + 2 = 0$ , what are the values of $a$ , $b$ , and $c$ , given $a x^{2} + b x + c = 0$ ?

Problem 2Multiple Choice

Solve $2 x^{2} - 5 x - 3 = 0$ using the quadratic formula and provide the solutions in simplest form.

Problem 3Multiple Choice

Solve $\frac{1}{2} x^{2} + 2 x - 3 = 0$ using the quadratic formula and simplify your answers.

Problem 4Multiple Choice

Compute the discriminant of $x^{2} - 8 x + 16 = 0$ and state how many real solutions the equation has.

Problem 5Multiple Choice

For the quadratic equation $4 x^{2} + x + 2 = 0$ , determine the discriminant and state the number of real solutions the equation has.

Problem 6Multiple Choice

Solve $3 x^{2} + 2 x - 8 = 0$ using the quadratic formula. Simplify all fractions to their lowest terms.

Problem 7Multiple Choice

Use the quadratic formula to solve $x^{2} - 4 x + 3 = 0$ .

Problem 8Multiple Choice

Use the quadratic formula to solve the equation $2 x^{2} + 3 x + 1 = 0$ .

Problem 9Multiple Choice

Which method is most efficient to solve $x^{2} + 6 x + 1 = 0$ , and why?

Problem 10Multiple Choice

Which method is most efficient for solving $(x + 3)^{2} - 4 = 0$ ?

Problem 11Multiple Choice

Solve $x^{2} + 6 x + 1 = 0$ using the quadratic formula.

Problem 12Multiple Choice

Why is completing the square particularly convenient when a = 1 and b is even?

Problem 13Multiple Choice

Find the complex roots of $x^{2} + 4 x + 13 = 0$ and express them in the simplest $a + b i$ form.

Problem 14Multiple Choice

Solve $2 x^{2} + 4 x + 7 = 0$ and give the roots in simplest $a + b i$ form.

Problem 15Multiple Choice

A projectile's height (in meters) after $t$ seconds is modeled by $h (t) = - 5 t^{2} + 20 t + 15$ . Use the quadratic formula to find when $h of t equals 0$ . Identify which (if any) is physically meaningful.

Problem 16Multiple Choice

Which method is the quickest to solve $3 x^{2} - 27 = 0$ , and why?

Problem 17Multiple Choice

For $2 x^{2} + 7 x + 3 = 0$ , which method is generally most efficient and why?

Problem 18Multiple Choice

Solve $2 x^{2} + 8 x + 6 = 0$ using the quadratic formula.

Problem 19Multiple Choice

Solve $x^{2} + 2 x + 5 = 0$ using the quadratic formula.

Problem 20Multiple Choice

Solve $4 x^{2} - 4 x + 1 = 0$ .

Problem 21Multiple Choice

For $5 x^{2} + 2 x + 1 = 0$ , determine the discriminant and state how many real solutions exist.

Problem 22Multiple Choice

A small business models profit as $P (x) = - x^{2} + 40 x - 375$ , where $x$ is the number of thousands of units sold. For which production levels $x$ does the profit equal zero? Use the quadratic formula and provide solutions in exact form.