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Standard Form of a Quadratic Function

Rule

Standard Form of a Quadratic Function

A quadratic function can be written in standard form as follows.

y=ax2+bx+cy=ax^2+bx+c

Here, a,a, b,b, and cc can be any real number, and a0.a\neq 0. When written in standard form, it's possible to use a,a, b,b, and cc to determine characteristics of a quadratic function. direction:upward when a>0,:downward when a<0y-intercept:(0,c)axis of symmetry:x=-b2a\begin{aligned} \textbf{direction} &: \text{upward when } a>0, \\ &\phantom{:} \text{downward when } a<0 \\ \mathbf{y} \textbf{-intercept} &: (0,c) \\ \textbf{axis of symmetry} &: x=\text{-}\dfrac{b}{2a} \end{aligned}