Quadratic Functions Key Characteristics

(4,-4)

(2,0)

(0,2)

(6,0)

maximum

minimum

neither

both

max/ opens down

min/ opens up

max/ opens up

min/ opens down

Vertex: (-2, 16); Axis of Symmetry: x = -2

Vertex: (2, 0); Axis of Symmetry: x = 2

Vertex: (2, 4); Axis of Symmetry: x = 2

Vertex: (-2, 4); Axis of Symmetry: z = --2

(0, 4)

x = 2

(4, 0)

x = -2

(2, 6)

(5, 0)

Vertex, axis of symmetry, and intercepts

Slope, intercepts, and degree

Degree, leading coefficient, and discriminant

Slope, vertex, and discriminant

opens up with a maximum

opens up with a minimum

opens down with a maximum

opens down with a minimum 

The highest or lowest point

The line of reflection of a quadratic function

$$x=\frac{-b}{2a}$$

The shape of a quadratic function

$$Ax^2+Bx+C$$

Opens up with a minimum

Opens down with a maximum

Opens left

Opens right

The highest or lowest point on the graph.

Where the parabola touches or intersects the x-axis.

Where the parabola touches or intersects the y-axis.

A line that divides the graph into two equal parts. i.e. cuts the graph in half.