Standard form of a quadratic function

Definition

The standard form of a quadratic function is given by $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq 0$. This form is useful for identifying the coefficients directly.

5 Must Know Facts For Your Next Test

1. It can be used to find the vertex of the quadratic by completing the square or using the vertex formula.
2. The direction of the parabola (upwards or downwards) is determined by the sign of coefficient $a$.
3. The y-intercept of the graph is at $(0, c)$.
4. The roots (or zeros) can be found using factoring, completing the square, or the quadratic formula.
5. The discriminant ($b^2 - 4ac$) indicates the nature and number of roots.

Related terms

Vertex Form:

A form of a quadratic function given by $f(x) = a(x-h)^2 + k$, where $(h,k)$ is the vertex.

Factored Form: A form of a quadratic function given by $f(x) = a(x-r_1)(x-r_2)$, where $r_1$ and $r_2$ are the roots.

Discriminant:

The expression $b^2 - 4ac$ used to determine the nature and number of roots of a quadratic equation.