Parabola
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A parabola is the U-shaped graph of a quadratic function. It is the graph of any quadratic equation, which is generally written in the form:
y = ax^2 + bx + c
where a, b, and c are constants, and a does not equal 0 (because if a = 0, the equation would no longer be quadratic).
Key characteristics of a parabola:
Shape: The graph of a quadratic function is a curve that can either open upward (if a > 0) or downward (if a < 0).
Vertex: The point at which the parabola reaches its highest or lowest value. It is the minimum point for parabolas that open upward and the maximum point for parabolas that open downward.
Axis of symmetry: A vertical line that passes through the vertex and divides the parabola into two symmetrical halves.
Direction: Parabolas that open upward have arms that move away from the vertex as they go upward, and parabolas that open downward have arms that move away from the vertex as they go downward.
Example:
For the quadratic equation y = x^2 - 4x + 3, the graph will be a parabola that opens upward, with the vertex being the lowest point on the curve.
In summary, a parabola is the shape created by plotting a quadratic function, and its direction (upward or downward) depends on the sign of the coefficient a.