Quadratic function
Quadratic function graph
The graph of a quadratic function is a parabola. To draw it, it is useful to know the vertex, axis of symmetry, roots, and a few points from a table.
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How do you draw a parabola?
- 1Check the sign of a to know whether the arms go up or down.
- 2Calculate the vertex and draw the axis of symmetry.
- 3Find the roots or choose points on both sides of the axis of symmetry.
- 4Mark the points and draw a smooth parabola through them.
Value table
For the function y = x² - 2x - 3, we choose x values on both sides of the axis of symmetry x = 1.
| x | y = x² - 2x - 3 | Point |
|---|---|---|
| -1 | 0 | (-1, 0) |
| 0 | -3 | (0, -3) |
| 1 | -4 | (1, -4) |
| 2 | -3 | (2, -3) |
| 3 | 0 | (3, 0) |
Function on the graph
The points from the table are symmetric with respect to the line x = 1. The vertex W = (1, -4) is the lowest point because a = 1 is positive.
The function decreases for x < 1 and increases for x > 1.
y = x² - 2x - 3
Vertex and axis of symmetry
The vertex is the turning point of the parabola. A vertical axis of symmetry passes through this point and divides the graph into two mirror-image parts.
Maximum and minimum values
a > 0
The parabola has its minimum value at the vertex.
a < 0
The parabola has its maximum value at the vertex.