A marathon of tension-filled reality shows can’t deliver the drama of quadratic functions. Peaks, valleys, hitting rock bottom – these plot twists do not exclusively belong to Hollywood. Quadratic functions depict the changing behavior of a set of data. Refer to the graph, Pop Star’s Record Sales.
Click More Images for a better view of the graph. Within 3 years after she inked her 1st record deal, the singer had sold over 15 million records in 1 year. Two years later, the pop fizzled and she sold zero records. Algebra can depict a rags to riches to rags spectacle better than any melodrama.
Characteristics of Quadratic Functions
1. Standard form is y = ax2 + bx + c, where a≠ 0.
2. The graph is a parabola, a u-shaped figure.
3. The parabola will open upward or downward.
4. A parabola that opens upward contains a vertex that is a minimum point.
A parabola that opens downward contains a vertex that is a maximum point.
Click , to view Parabola that opens upward and Parabola that opens downward.
5. The domain of a quadratic function is all real numbers.
6. To determine the range of a quadratic function, ask yourself
two questions:
- Is the vertex a minimum or
maximum? - What is the y-value of the vertex?
If the vertex is a minimum, then the range is all real numbers greater than or equal to the y-value.
If the vertex is a maximum, then the range is all real numbers less than or equal to the y-value.
7. An axis of symmetry (also known as a line of symmetry) will divide the parabola into mirror images. The line of symmetry is always a vertical line of the form x = n, where n is a real number. Click More Images to view Parabola that opens upward. Its axis of symmetry is the vertical line x =0.
8. The x-intercepts are the points at which a parabola intersects the x-axis. These points are also known as zeroes, roots, solutions, and solution sets. Each quadratic function will have two, one, or no x-intercepts.