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