Opening Downward (Quadratic Functions)
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 quadratic function opens downward when the graph of the quadratic equation is shaped like an "n" or an upside-down "U". This occurs when the coefficient a of the quadratic term x2 in the standard form equation y = ax^2 + bx + c is negative (i.e., a < 0).
Key points about a quadratic opening downward:
The parabola opens downward if a < 0.
The vertex of the parabola represents the maximum point, meaning it is the highest point on the graph.
The arms of the parabola move away from the vertex as they extend, creating the "n" shape.
Example:
For the quadratic equation y = -3x^2 + 6x + 2, the coefficient a = -3 is negative, so the parabola opens downward. The vertex will represent the maximum point, and the parabola will continue to descend as you move away from the vertex.