Functions
8-8Linear and Quadratic Functions
Overview
Linear: f(x) = mx + b, graph is a line. Quadratic: f(x) = ax² + bx + c, graph is a parabola.
Key ideas
- Linear functions have constant rate of change.
- Quadratic functions have a vertex (max or min).
- Parabola opens up if a > 0, down if a < 0.
Worked examples
Example 1
Problem. Classify f(x) = 2x − 7.
Solution. Linear.
Example 2
Problem. Classify g(x) = x^2 − 4.
Solution. Quadratic; parabola opens up.
Practice
Try each one. Click Show answer when ready.
- 1.
Classify f(x) = −3x + 1.
- 2.
Classify h(x) = 2x^2 + x.
- 3.
Does y = x^2 − 1 open up or down?
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Graph y = x² − 4x + 3. Find the vertex and x-intercepts.
- 2.
Is y = 2x² − 8x + 5 a linear or quadratic function? How do you know?