Final answer:
The maximum and minimum of quadratic functions can be determined using the vertex formula. The vertex formula calculates the coordinates of the vertex of a quadratic function and helps in finding the maximum or minimum value.
Step-by-step explanation:
The maximum and minimum of quadratic functions can be determined using the vertex formula. The vertex formula, also known as the Quadratic Extremum Rule, calculates the coordinates of the vertex of a quadratic function. To find the maximum or minimum value, you need to determine whether the parabola opens upwards or downwards.
If the parabola opens upwards (a > 0), then the vertex represents the minimum point of the function. If the parabola opens downwards (a < 0), then the vertex represents the maximum point of the function.
The vertex of a quadratic function with the equation ax² + bx + c = 0 can be calculated using the formula:
x = -b / (2a)
Once you have the x-coordinate of the vertex, you can substitute it back into the quadratic function to find the corresponding y-coordinate.