1. Calculate points from this table and plot the points as you go.x y
The basic parabola is shown on the graph, dotted blue.
Draw a parabola through the points.
Adding 2 to x2 moves the basic parabola
up by 2 units.
How?

2. x y
Calculate points from this table and plot.
The basic parabola is shown on the graph, dotted blue.
Draw a parabola through the points.
Subtracting 3 from x2 moves the basic parabola
down by 3 units.
How?

3. x y
Calculate points from this table and plot.
The basic parabola is shown on the graph, dotted blue.
Draw a parabola through the points.
Adding 4 to x and then squaring moves the basic parabola
How?
to the left by 4 units.

4. x y
Calculate points from this table and plot.
Draw a parabola through the points.
The basic parabola is shown on the graph, dotted blue.
Subtracting 1 from x and then squaring moves the basic parabola
How?
to the right by 1 unit.

5. y
parabola
the
moves 2
The -
2 units to the right.
How? x

6. y
parabola
the
moves 3
The -
3 units down.
How? x

7. x y
Calculate points from this table and plot.
The basic parabola is shown on the graph, dotted blue.
Draw a parabola through the points.
Multiplying x2 by 2 makes the basic parabola
steeper.
What?

8. x y
Calculate points from this table.
The basic parabola is shown on the graph, dotted blue
Draw a parabola through the points.
Multiplying x2 by makes the basic parabola
wider.
What?

9. y
The x2 means the parabola is
upside down.
What? x

10. y
The 4 means the parabola is moved
How?
up by 4 units. x

11. y
The –(….)2 means the parabola is
upside down.
What? x

12. y x
The 2 means the parabola is moved
left by 2 units.
How?

13. y
The –(….)2 means the parabola is
upside down.
What? x

14. The –1 means the parabola is moved
right by 1 unit.
How? x

15. The –2 means the parabola is moved
How?
down by 2 units. x

16. x y
Calculate points from this table & plot.
Draw a parabola through the points.
The graph shows the parabola cuts the x-axis at 3 and –1.
Continued on next slide.

17. y
The x-intercepts can be obtained from the two factors:
At x-intercepts, y = 0.
Solve. x
Coordinates of the x-intercepts are (3,0) and (1,0).

18. y
Factorise
Equate to 0 for x-intercepts
Solve.
Substitute x = 0 for y-intercept
Draw a parabola through the points.
The line of symmetry of the parabola is halfway between x = 4 and x = 2. x
i.e. x = 1.
Substitute x = 1 for y-coordinate of vertex
The vertex is at

19. y
Equate to 0 for x-intercepts
Solve.
Substitute x = 0 for y-intercept
Draw a parabola through the points.
The line of symmetry of the parabola is halfway between x = 0 and x = 4. x
i.e. x = 2.
Substitute x = 2 for y-coordinate of vertex
The vertex is at

20. y
Equate to 0 for x-intercepts
Solve.
Note: The position of the vertex means the graph must be upside down.
Substitute x = 0 for y-intercept
Draw a parabola through the points.
The line of symmetry of the parabola is halfway between x = 1 and x = 5. x
i.e. x = 3.
Substitute x = 3 for y-coordinate of vertex
The vertex is at