Question

What is the vertex of `y= 3(x - 1)^2 + 1`?

Answer 1

The vertex for this parabola is `(1,1)`.

Explanation:

This is an equation for a parabola. `y=3(x-1)^2+1` is in vertex form, `y=a(x-h)^2+k`, where `a=3, x=h, k=1`

The vertex is the minimum or maximum point on the parabola. In this case the vertex is the minimum point because `a` is greater than one, so the parabola opens upward.

The axis of symmetry is the vertical line, `x`, that divides the parabola into two equal halves. In vertex form, the axis of symmetry is designated as `(x=h)`, so `(x=1)`.

The vertex point in vertex form is `(h,k)`, which is `(1,1)`.

Resource: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

graph{y=3(x-1)^2+1 [-10, 10, -5, 5]}