SAT Math

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

Numbers and OperationsAlgebraic Expressions and EquationsLinear Functions and Graphs
Quadratic Functions and ParabolasSystems of EquationsData Analysis and Statistics
Budgeting and Financial MathDistance, Rate, and Time ProblemsGeometry in Construction and Design
Plugging In NumbersBacksolving Answer Choices
Numbers and Operatio...Algebraic Expression...Linear Functions and...Quadratic Functions ...Systems of EquationsData Analysis and St...Budgeting and Financ...Distance, Rate, and ...Geometry in Construc...Plugging In NumbersBacksolving Answer C...
Advanced Topics

Quadratic Functions and Parabolas

Quadratic Functions

Quadratic functions look like \( y = ax^2 + bx + c \) and graph as parabolas (U-shaped curves). The SAT tests your ability to factor, solve, and interpret these equations.

Vertex and Axis of Symmetry

The vertex is the highest or lowest point on the graph, and the axis of symmetry is the vertical line that passes through the vertex.

Factoring and Solutions

You can solve quadratics by factoring, using the quadratic formula, or completing the square.

Real-World Applications

Quadratics show up in projectile motion, area problems, and optimization scenarios.

Must-Know

  • The graph opens upward if \( a > 0 \) and downward if \( a < 0 \).
  • The vertex formula: \( x = -\frac{b}{2a} \)

Key Formula

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

Examples

  • Solving \( x^2 - 5x + 6 = 0 \) by factoring: \( (x-2)(x-3) = 0 \) so \( x = 2 \) or \( x = 3 \)

  • Finding the vertex of \( y = 2x^2 - 4x + 1 \): \( x = \frac{4}{4} = 1 \)

In a Nutshell

Quadratic functions model curves and help solve real-world problems involving change.

Key Terms

Parabola
The U-shaped graph made by a quadratic function.
Vertex
The turning point of a parabola.
Next
Systems of Equations