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What is the discriminant in algebra?

Demonstrate an understanding of the absolute value of real numbers

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Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

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 that involve 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

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Rationalize the denominator

Solve problems that involve 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 limited to 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 limited to 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 that involve rational equations limited to 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 quadratic functions of the form y = a(x - p)^2 + q and determine characteristics

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

Analyze quadratic functions of the form y = ax^2 + bx + c to identify characteristics and solve problems

Introduction to quadratic functions

Characteristics of 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

Completing the square

Completing the Square

Solve problems that involve 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 that involve systems of linear-quadratic and quadratic-quadratic equations in two variables

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Solve problems that involve linear and quadratic inequalities in two variables

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

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 that involve quadratic inequalities in one variable

Solving quadratic inequalities

Demonstrate an understanding of angles in standard position 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

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Use tangent ratio to calculate angles and sides (Tan = o / a)

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Pre-Calculus 110

Algebra and Number

Relations and Functions

math

Ex.1

Ex.2

Ex.3

The discriminant is actually part of the quadratic formula. It is super useful when we only need to determine whether a quadratic equation has 2 real solutions, 1 real solution, or 2 complex solutions.

Nature of roots of quadratic equations: the discriminant

The discriminant: Nature of roots of quadratic equations

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

Solving quadratic equations using the quadratic formula