Maximum (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
The maximum of a quadratic function refers to the highest point on the graph of the parabola. This occurs when the parabola opens downward, which happens when the coefficient a in the quadratic equation y = ax^2 + bx + c is negative.
The maximum value corresponds to the y-coordinate of the vertex, which is the point where the parabola reaches its highest value. The x-coordinate of the vertex gives the value of x at which the maximum occurs.
Key points about the maximum:
A quadratic has a maximum if it opens downwards (i.e., a < 0).
The maximum value is the y-coordinate of the vertex.
The x-coordinate of the vertex gives the value of x at which the maximum occurs.
Example:
For the quadratic equation y = -2(x - 3)^2 + 5, the vertex form shows that:
The parabola opens downward because a = -2 is negative.
The vertex is at (3, 5), so the maximum value is 5, and it occurs at x = 3.