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Quadratic Function Example 1

This example is to description how to draw the graph of the quadratic function y = x2 - 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 = x2 - 4x + 5
= x2 - 4x + 22 - 22 + 5
= x2 - 4x + 4 - 4 + 5
= x2 - 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 = ax2 + bx + x, where the coefficient a can not be zero, is the set of points (x, y) that satisfy the quadratic function y = ax2 + 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 = x2 - 4x + 5.