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f(x)=ax^2+bx+c
Here, a, b, and c are real numbers with a≠ 0. The term with the highest degree — the quadratic term — is written first, then the linear term, followed by the constant term. The standard form of the function can be used to determine the direction of the parabola, the y-intercept, the axis of symmetry, and the vertex.
| Direction of the Graph | Opens upward when a> 0 |
|---|---|
| Opens downward when a< 0 | |
| y-intercept | c |
| Axis of Symmetry | x = -b/2a |
| Vertex | (-b/2a,f(-b/2a)) |
Similar to a quadratic function, a quadratic equation can be written in standard form. This is called the standard form of a quadratic equation. ax^2 + bx + c = 0 In this equation, a is not equal to 0. The solutions of a quadratic equation written in this form can be found by applying the Quadratic Formula.
Both the vertex and intercept forms of a quadratic function can always be rewritten in standard form.
| Form | Equation | How to Rewrite? |
|---|---|---|
| Vertex Form | y = a(x-h)^2+k | Expand (x-h)^2, distribute a, and combine like terms. |
| Intercept Form (also called Factored Form) |
y = a(x-p)(x-q) | Multiply a(x-p)(x-q) and combine like terms. |