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## Quadratic Function Example 1

This example is to description how to draw the graph of the quadratic function y = x^{2} - 4x + 5. First, we need to find the vertex of the graph of the quadratic function.
To find the vertex of this graph, we need to use the formula of the completing the square.

- y = x
^{2}- 4x + 5 - = x
^{2}- 4x + 2^{2}- 2^{2}+ 5 - = x
^{2}- 4x + 4 - 4 + 5 - = x
^{2}- 4x + 4 + 1 - = (x - 2)
^{2}+ 1

Therefore, the vertex of the quadratic function is (2, 1), the axis of symmetry of the graph is x = 2.

Note: If the quadratic function is written in the form y = a(x - h)^{2} + k, then the vertex is (h, k), the axis of symmetry is x = h.

The graph of the quadratic function y = ax^{2} + bx + x, where the coefficient a can not be zero, is the set of points (x, y) that satisfy the quadratic function
y = ax^{2} + bx + c. Because the coefficient a is larger than zero, so the graph is open upward. So x = 2 is the minimum value of the quadratic function.
We let x = 2 be the middle value of the set of x.

x | ... | 0 | 1 | 2 | 3 | 4 | ... | |
---|---|---|---|---|---|---|---|---|

y | ... | 5 | 2 | 1 | 2 | 5 | ... |

You can choose as many values of x as you like and calculate the value of y to get the set of points (x, y), then connect those points to get the graph of the quadratic function y = x^{2} - 4x + 5.