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.