Home > Subjects > Mathematics > Level 1 > 1.2 Graphs (AS90148) > Subject content > Graphing parabolas
- Subject: Mathematics
- AS: 90148
- Level: 1
- Credits: 3
- External
Mathematics 1.2 Sketch and interpret graphs
Graphing parabolas
Graphing parabolas by plotting points
If an accurate graph is required plot points by drawing up a table of values. To do this:
- Use the values on the horizontal axis for the first row.
- Substitute in these numbers into the equation to work out the other coordinate.
- Plot the points and join them together with a smooth curve.
- Draw a rounded turning point.
Example
Draw the graph of y = x(x – 4) from x = 0 to x = 4
First draw up a table for each of the x values and work out the y-value for each by substituting the number for x in the equation.
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 0 | -3 | -4 | -3 | 0 |
Plot these points and join with a smooth curve.
Round the turning point.
For more information see:
Graphing Quadratic Equations I
Graphing Parabolas
Practice with Parabolas
Graphing parabolas by using transformations
The basic parabola y = x2 can be transformed in the following ways:
- y = x2 + 2 moves y = x2 up 2 units
- y = x2 – 2 moves y = x2 down 2 units
- y = (x – 2)2 moves y = x2 to the right 2 units
- y = (x + 2)2 moves y = x2 to the left 2 units
- y = - x2 reflects y = x2 in the x-axis (it’s upside down)
For more information on transforming graphs see:
Function transformations I
Graphs of quadratic functions
Quadratic functions (Java™ required)
Slider graph (Java™ required)
Graphing parabolas by using intercepts
- To find where the graph cuts the x-axis, put y = 0 in the equation.
- To find the y-intercepts, put x = 0 in the equation.
- The axis of symmetry is halfway between the x-intercepts. Write an equation x = ?, The ? is where the line cuts the x-axis.
- The vertex has the same x-coordinate as the axis of symmetry.
- To find the y-intercept of the vertex, put the x-coordinate into the equation and calculate y.
For more information on using intercepts, see:
Curved graphs
S-cool maths GCSE graphs
Slider graph (Java™ required)
Parabolas in vertex form (Java™ required)
