Algebra & Functions

Quadratic Functions

Parabolas, roots, turning points and discriminant.

Standard form

\[f(x)=ax^2+bx+c\]

If \(a>0\), the parabola opens upward. If \(a<0\), it opens downward.

The vertex lies on the axis of symmetry \(x=-rac b{2a}\).

Find the roots of \(x^2-5x+6=0\).

\[x^2-5x+6=(x-2)(x-3)\]

So the roots are \(x=2\) and \(x=3\).