Opening Upward (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 upward when the graph of the quadratic equation is shaped like a "U". This occurs when the coefficient a of the quadratic term x^2 in the standard form equation y = ax^2 + bx + c is positive (i.e., a > 0).
Key points about a quadratic opening upward:
The parabola opens upward if a > 0.
The vertex of the parabola represents the minimum point, meaning it is the lowest point on the graph.
The arms of the parabola move away from the vertex as they extend, creating the "U" shape.
Example:
For the quadratic equation y = 2x^2 - 4x + 1, the coefficient a = 2 is positive, so the parabola opens upward. The vertex will represent the minimum point, and the parabola will continue to rise as you move away from the vertex.