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A quadratic function is a polynomial function of degree 2 that can always be written in the form y=ax^2+bx+c, with a≠ 0. Notice that the highest exponent of the independent variable is 2. The graph of any quadratic function is a vertical parabola.
There are three ways to write a quadratic function.
| Name | Equation | Characteristics |
|---|---|---|
| Standard Form | y=ax^2+bx+c | a, b, and c are real numbers, a≠ 0, and c is the y-intercept of the parabola. |
| Vertex Form | y=a(x-h)^2+k | a, h, and k are real numbers, a≠ 0, and (h,k) is the vertex of the parabola. |
| Intercept Form (also called Factored Form) |
y=a(x-x_1)(x-x_2) | a, x_1, and x_2 are real numbers, a≠ 0, and x_1 and x_2 are the x-intercepts of the parabola. |