1. Graphing Quadratics

2. Parabolas Any equation, where the highest power of x, is x2
when plotted on a graph, will form a parabola
The simplest parabola is x -3 -2 -1 1 2 3
y=x2 9 4 1 1 4 9
We can see the shape looks like:
Starting at the vertex
Out 1 up 12
Out 2 up 22
Out 3 up 32
Out 4 up 42

3. x -3 -2 -1 1 2 3
y = -x2 -9 -4 -0
The graph is the same shape but upside-down
The negative sign reflects the graph in the x axis

4. We can see the larger the number in front of the x2
The steeper the graph
Remember the slope of linear graphs got steeper if we increased the number by the x
These graphs are best plotted using points

5. x
y=x2
y =2x2
Y=3x2 1 2 4 3 9 2 3 8 12 18 27

6. The graph is still reflected in the x axis
We can see the larger the number in front of the x2
The steeper the graph
Remember the gradient of linear graphs got steeper if we increased the number by the x

7. The smaller the number in front of the x2 the flatter the graph
The ones with negative sign are reflected in the x axis

8. If we add a number to the x2 the parabola shifts up
We can see:
If we add a number to the x2 the parabola shifts up
If we subtract a number from the x2 the parabola shifts down
Note the shape is the basic
Remember the correct word for shift is translate

9. We can also add numbers to the x before it is squared
We can see the shape is the basic x2 shape
If we add a number in the brackets the
graph is translated to the left by the magnitude of the number
If we subtract a number in the brackets
the graph is translated to the right by the magnitude of the number

10. If we add a number in the brackets and at the end the graph is translated
vertically and horizontally

11. We can also translate the reflected graphs

12. To draw Parabolas: Decide how it has been translated (find vertex)
Decide if reflected in x axis (a<0)
Stretched or compressed?
Draw appropriate y = ax2 type from new vertex.

13. Parabolas in factorised form

15. E.g. 3

16. End Lesson Graphing Quadratics
Homework: Page 47 #1-4, 9, 10.