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