How do you find the vertex of a parabola f(x)=x22x3?

1 Answer
Jul 10, 2015

The vertex of f(x) is 4 when x=1 graph{x^2-2x-3 [-8, 12, -8.68, 1.32]}

Explanation:

Let a,b,c, 3 numbers with a0

Let p a parabolic function such as p(x)=ax2+bx+c

A parabola always admit a minimum or a maximum (= his vertex).

We have a formula to find easily the abscissa of a vertex of a parabola :

Abscissa of vertex of p(x)=b2a



Then, the vertex of f(x) is when (2)2=1

And f(1)=123=4


Therefore the vertex of f(x) is 4 when x=1

Because a>0 here, the vertex is a minimum.