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ANSWER

The vertex is (-2,1)

EXPLANATION

We want to find the vertex of

[tex]y = {x}^{2} + 4x + 5[/tex]

We complete the square to obtain,

[tex]y = {x}^{2} + 4x + {(2})^{2} - {(2})^{2} + 5[/tex]

The first three terms forms a perfect square trinomial.

[tex]y = {(x + 2})^{2} - 4 + 5[/tex]

The vertex form is

[tex]y = {(x + 2})^{2} + 1[/tex]


This equation is in the form;

[tex]y = a{(x -h})^{2} + k[/tex]


where (h,k)=(-2,1) is the vertex.

Answer:

-2,1

Step-by-step explanation:

Plug into  y = x^2 + 4x + 5 calculator in y equals and then press second (blue button) graph (table/f5). Scroll down the chart until you see the middle of a pattern. You will see

5

2

1

2

5

In the middle of the pattern you will find the y-coordinate, and if you look a little to the left, you will also see the x coordinate. Hope this helps!

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