About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

The basic characteristics of quadratic functions

Demonstrate an understanding of the absolute value of real numbers

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

auto-gen

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Solve problems involving operations on radicals and radical expressions with numerical and variable radicands

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Solve problems involving radical equations limited to square roots

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Determine equivalent forms of rational expressions with numerators and denominators that are monomials, binomials or trinomials

Partial fraction decomposition

Simplifying rational expressions and restrictions

Simplifying complex fractions

Perform operations on rational expressions with numerators and denominators that are monomials, binomials or trinomials

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Solve problems involving rational equations with numerators and denominators that are monomials, binomials or trinomials

Solving rational equations

Applications of rational equations

Factor polynomial expressions of various forms

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyze geometric sequences and series to solve problems

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Graph and analyze reciprocal functions limited to the reciprocal of linear and quadratic functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Analyze quadratic functions of the form y = a(x - p)² + q and determine characteristics of the corresponding graph

Characteristics of quadratic functions

Transformations of quadratic functions

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph

Introduction to quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Solve problems involving quadratic equations

Solving polynomial equations by iteration

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solve algebraically and graphically problems involving systems of linear-quadratic and quadratic-quadratic equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Solve problems involving linear and quadratic inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Solve problems involving quadratic inequalities in one variable

Solving quadratic inequalities

Analyze arithmetic sequences and series to solve problems

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Demonstrate an understanding of angles in standard position from 0° to 360°

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Solve problems using the three primary trigonometric ratios for angles from 0° to 360° in standard position

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Solve problems using the cosine law and sine law, including the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Grade 11 Pre-Calculus Mathematics (30S)

Develop algebraic reasoning and number sense

Develop algebraic and graphical reasoning through the study of relations

Develop trigonometric reasoning

math

Ex. 2

Finding vertex, intercepts, and graphing a quadratic in vertex form

Ex.3

Finding intercepts, vertex, and sketching a quadratic graph

Ex.4

Finding vertex, intercepts, and graphing from vertex form

Ex. 1

Identifying vertex, axis of symmetry, intercepts, domain, and range

Analyzing a downward-opening parabola with no x-intercepts

Using the quadratic formula to find x-intercepts and graph the parabola

Finding characteristics of y = -2x² + 4x + 6

Finding x-intercepts and vertex using completing the square

Graphing a downward-opening parabola using the vertex formula

Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a <a href='[[glossary.html|{"keyword":"Parabola"}]]'>parabola</a> that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.

Properties and graphs of quadratic functions

Solving quadratic equations using the quadratic formula

Characteristics of quadratic functions

What You'll Learn

Identify the vertex as the highest or lowest point on a parabola

Recognize that quadratic functions always have a domain of all real numbers

Determine the axis of symmetry as a vertical line through the vertex

Locate x-intercepts and y-intercepts on the parabola

Distinguish between maximum and minimum values based on parabola direction

Calculate the range based on the vertex and direction of opening

What You'll Practice

Finding vertex coordinates from parabola graphs

Determining whether parabolas open upward or downward

Calculating x-intercepts and y-intercepts algebraically

Writing equations for axis of symmetry

Identifying domain and range from graphs

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

10 Video lessons

Skills

Parabola

Vertex

Domain and Range

Axis of Symmetry

Intercepts

End Behavior

Quadratic Functions