Quadratic Function Example 1
This example is to description how to draw the graph of the quadratic function y = -2x2 - 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 = -2x2 - 8x + 1
- = -2(x2 + 4x) + 1
- = -2(x2 + 4x + 4 - 4) + 1
- = -2(x2 + 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 = ax2 + bx + x, where the coefficient a cannot be zero, is the set of points (x, y) that satisfy the quadratic function
y = ax2 + 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 = -2x2 - 8x + 1.