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

Answer:

$(0,2)$; minimum

Step-by-step 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.