Definition
• A quadratic function is a function of the form
f(x) = ax² + bx + c, where a ≠ 0.
Standard Form
• The standard form of a quadratic function is
f(x) = ax² + bx + c.
Graph Shape
• The graph of a quadratic function is a
parabola. It opens upward if a > 0 and
downward if a < 0.
Vertex
• The vertex is the highest or lowest point of the
parabola, located at x = -b/(2a).
Axis of Symmetry
• The axis of symmetry is a vertical line that
passes through the vertex: x = -b/(2a).
Intercepts
• Y-intercept: (0, c)
• X-intercepts: Solve ax² + bx + c = 0 using
factoring, completing the square, or the
quadratic formula.
Domain and Range
• Domain: All real numbers
• Range: Depends on the direction of the
parabola (upward or downward).
Symmetry
• The graph is symmetric about the axis of
symmetry.