Question

Graph y = x2 + 2. Identify the vertex of the graph. Tell whether it is a minimum or maximum. (0, 2); maximum (0, 2); minimum (2, 0); maximum (2, 0); minimum

Answer 1

`(0,2)`; minimum

Explanation:

Given:

The function is,
`y=x^(2)+2`

The given function represent a parabola and can be expressed in vertex form as:

`y=(x-0)^(2)+2`

The vertex form of a parabola is
`y=(x-h)^(2)+k`, where,
`(h,k)` is the vertex.

So, the vertex is
`(0,2)`.

In order to graph the given parabola, we find some points on it.

Let
`x=-2,y=(-2)^(2)+2=4+2=6`

`x=-1,y=(-1)^(2)+2=1+2=3`

`x=0,y=(0)^(2)+2=0+2=2`

`x=2,y=(2)^(2)+2=4+2=6`

`x=1,y=(1)^(2)+2=1+2=3`

So, the points are
`(-2,6),(-1,3),(0,2),(1,3),(2,6)`.

Mark these points on the graph and join them using a smooth curve.

The graph is shown below.

From the graph, we conclude that at the vertex
`(0,2)`, it is minimum.