back to *algebra2 video lessons*
## Quadratic Function Example 1

This example is to description how to draw the graph of the quadratic function y = -2x^{2} - 8x + 1. 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 = -2x
^{2}- 8x + 1 - = -2(x
^{2}+ 4x) + 1 - = -2(x
^{2}+ 4x + 4 - 4) + 1 - = -2(x
^{2}+ 4x + 4 + 8 + 1 - = -2(x + 2)
^{2}+ 9

Therefore, the vertex of the quadratic function is (-2, 9), 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 less than zero, so the graph is open downward. So x = -2 is the maximum value of the quadratic function.
We let x = -2 be the middle value of the set of x.

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

y | ... | 1 | 7 | 9 | 7 | 1 | ... |

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 = -2x^{2} - 8x + 1.