Characteristics of Parabolas

Turning Point

Another description for "vertex"

Concave Down

The direction of a parabola with a maximum point as a vertex.

Concave Up

The direction of a parabola with a minimum point as a vertex.

Parabola

The general shape of the graph of a quadratic function.

Vertex

The highest or lowest point of a parabola.

x-intercept of a parabola

The point or points where a parabola crosses the x-axis. The y coordinates are zero.

y - intercept of a parabola

The point where a parabola crosses the y-axis. The x coordinate is zero.

Maximum

The vertex of a parabola that is the highest point.

Minimum

The vertex of a parabola that is the lowest point.

Axis of Symmetry

The vertical line that goes through the vertex of the parabola.

Cuts the parabola in half, vertically

What the "axis of symmetry" does to a parabola

The factored form (intercept form) of a quadratic function

f(x) = a(x - m)(x - n) where m, n are roots.

The vertex form of a quadratic function

f(x) = a(x-h)² + k

The standard form of a quadratic function

f(x) = ax² + bx + c

Other names for zeros of a function

roots, x-intercepts, solutions

Range of a Quadratic Function

the allowable y-values; if the vertex is a maximum, the range will be y ≤ k; if the vertex is a minimum, the range will be y ≥ k

Decreasing Interval

the part of the domain where the function decreases, as you read from left to right

Increasing Interval

the part of the domain where the function increases, as you read from left to right

Domain of a Quadratic Function

typically, all real numbers; the allowable x-values

The equation for the Axis of Symmetry, when the Quadratic Function is in Standard Form: y=ax²+bx+c

x = -b/2a