# Which is the graph of the function f(x) = x^{2 }+ 2x + 3?

**Solution:**

Given, the function is f(x) = x^{2} + 2x + 3

We have to find the graph of the function.

Let y = x^{2} + 2x + 3

Put x = -3

y = (-3)^{2} + 2(-3) + 3

= 9 - 6 + 3

= 9 - 3

y = 6

Put x = -2

y = (-2)^{2} + 2(-2) + 3

= 4 - 4 + 3

y = 3

Put x = -1

y = (-1)^{2} + 2(-1) + 3

= 1 - 2 + 3

= 4 - 2

y = 2

Put x = 0

y = (0)^{2} + 2(0) + 3

= 0 + 0 + 3

y = 3

Put x = 1

y = (1)^{2} + 2(1) + 3

= 1 + 2 + 3

= 3 + 3

y = 6

x | -3 | -2 | -1 | 0 | 1 |
---|---|---|---|---|---|

y | 6 | 3 | 2 | 3 | 6 |

We can plot the graph using the points.

Therefore, the graph is a parabola with vertex (-1, 2).

## Which is the graph of the function f(x) = x^{2} + 2x + 3?

**Summary:**

The graph of the function f(x) = x^{2} + 2x + 3 is a parabola with vertex (-1, 2).

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