What is a quadratic function?

A quadratic function is a function where the highest power of $x$ is 2.

The most common form is:

f(x)=ax^2 + bx + c

Where:

• a, $b$, and $c$ are numbers

• a≠0

Examples:

• x^2

• 2x^2 + 3x – 1

• -x^2 + 4

What does a quadratic graph look like?

The graph of a quadratic function is called a parabola.

Key features:

• U-shaped curve

• Opens up if a>0

• Opens down if a<0

• Has a vertex (highest or lowest point)

Important parts of a quadratic graph

1. Vertex

• The turning point of the parabola

• Lowest point if it opens up

• Highest point if it opens down

2. Axis of symmetry

• A vertical line that splits the parabola in half

• Formula:

x = −(b/2a)​

3. Intercepts

• y-intercept: where the graph crosses the y-axis

• x-intercepts (zeros): where the graph crosses the x-axis

Why quadratic functions matter

Quadratics model:

• Projectile motion

• Profit and revenue

• Area problems

• Physics and engineering situations