SAT Math

A comprehensive course to master all the mathematical concepts, skills, and strategies needed to succeed on the SAT exam.

Numbers and OperationsAlgebra and Linear EquationsData Analysis and Problem Solving
Quadratic Equations and PolynomialsFunctions and Nonlinear RelationshipsGeometry and Trigonometry
Budgeting and Financial MathInterpreting Data in the NewsMath in Sports and Design
Plugging In NumbersEliminating Wrong AnswersTime Management on the SAT
Numbers and Operatio...Algebra and Linear E...Data Analysis and Pr...Quadratic Equations ...Functions and Nonlin...Geometry and Trigono...Budgeting and Financ...Interpreting Data in...Math in Sports and D...Plugging In NumbersEliminating Wrong An...Time Management on t...
Advanced Topics

Quadratic Equations and Polynomials

Tackling Parabolas and Beyond

Quadratic equations are powerful tools for modeling situations with curved relationships, like projectile motion or profit problems.

Key Components

  • Standard Form: \( ax^2 + bx + c = 0 \)
  • Factoring: Rewrite quadratics as a product of two binomials.
  • Quadratic Formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
  • Vertex and Axis of Symmetry: Identify the highest or lowest point of the parabola.

Working with Polynomials

  • Add, subtract, and multiply polynomials.
  • Recognize patterns (difference of squares, perfect square trinomials).

Why It Matters

From designing roller coasters to planning business profits, quadratics show up everywhere.

Key Formula

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Examples

  • Solve \( x^2 - 5x + 6 = 0 \) by factoring.

  • Find the vertex of \( y = 2x^2 - 4x + 1 \ ).

In a Nutshell

Master quadratics to solve equations and model real-world curves.

Key Terms

Quadratic Equation
An equation where the highest exponent of the variable is 2.
Vertex
The maximum or minimum point of a parabola.
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Functions and Nonlinear Relationships
Quadratic Equations and Polynomials - SAT Math Content | Practice Hub