Algebra

Chapter 1

Algebra

Course: Sat Prep
Subject: Math
Chapter: Advanced Math

By the end of this lesson, you will be able to:

• Solve quadratic equations using multiple methods.
• Factor quadratic expressions.
• Complete the square.
• Apply the quadratic formula.
• Convert between standard form and vertex form.
• Graph quadratic functions.
• Identify the vertex, axis of symmetry, and intercepts.
• Determine maximum and minimum values.
• Model real-world situations using quadratic functions.

Quadratic equations and functions are among the most important topics on the Digital SAT. Unlike linear functions, which produce straight lines, quadratic functions produce curved graphs called parabolas. These functions model many real-world situations involving area, motion, profit, revenue, and optimization.

The general form of a quadratic function is

$\displaystyle \boxed{f(x)=ax^2+bx+c}$

where

$\displaystyle a\neq0$

and $a$, $b$, and $c$ are constants.

Examples:

$\displaystyle f(x)=x^2-4x+3$ $\displaystyle f(x)=2x^2+5x-7$ $\displaystyle f(x)=-3x^2+6x+1$

The graph of every quadratic function is a parabola.