The standard form of a quadratic function; the sign of a determines which way the parabola opens.
Symbols
a,b,c
coefficients (a=0)
x
argument
Where it comes from
The most basic way to write a quadratic function. The coefficient a sets the shape: a>0 — opens upward (minimum), a<0 — opens downward (maximum). c is the y-intercept.
When to use it
The starting point — from it we compute the discriminant, vertex, and roots.
Example
State the direction the parabola opens and its y-intercept for f(x)=2x2−3x+1.