1. Graphs

2. Parabola

3. y = (x+3)2
y = x2
y = x2+1
y = x2-2
y = x2+3

4. Find the equation of the graph using
The equation is
y = a (x – 2 ) ( x + 5)
Using the point ( 0 , -5)
The final equation is
y = ½ ( x – 2 ) ( x + 5 ) -5 2 -5
Find the equation of the graph using
y = a ( x + b ) ( x + c )

5. y = ½ ( x – 2 ) ( x + 5 )
y = ½ ( x – 3 ) ( x + 4 )
y = ½ ( x – 2 ) ( x + 5 ) + 5

6. Hyperbola

7. y = or xy = 1
(1 , 1)
Asymptote at y = 0
(-1 , -1)

8. Asymptote down x = 0 (1 , 3) (graph has Asymptote along y = 2 (-1 , 1)
y=1/x
Asymptote down x = 0
(1 , 3) (graph has
moved up 2)
Asymptote
along y = 2
(-1 , 1)

9. Asymptote down x = 3 (-2 , 1) (graph has moved Asymptote along y = 0
y=1/x
Asymptote down x = 3
(-2 , 1) (graph has moved
to the left 3 places)
Asymptote along y = 0
(- 4 , -1)

10. Exponential

11. y = 2x
y = 3x
(0,1)
Exponential functions illustrate growth and decline.
When x = 0, y = a0 = 1, so the y-intercept of basic exponential functions is (0,1) for any value of a.
The graph has no x-intercept because the equation ax =0 has no solution.

12. y = 2x + 1
(0,2)

13. y = 2(x+1)
y = 2(x+2)

14. Y-intercept is (0,2), so y = 2ax
(1,6) is on the graph
6 = 2 x a a = 3
Equation: y = 2(3x)

15. Write the equations for the following graphs
Y = 2x, exponential
Some coordinates other than (0,1) ie.(1,2) (2,4) (3,8)
General graph is
y = ax putting (3,8) in we get 8 = a3 and solve for a. a=2
Then check with another point
Write the equations for the following graphs
y = (x+1)(x-2)2
One of the turning points is on the x axis and the other cutting through the x axis
xy= - 4, hyperbola
Drawn in second and forth quadrants therefore in the form xy = - a. Passes through points (-1,4) & (-2, 2)

16. Trig graphs

17. y = sin x
y = sin ( x + π/2 )

18. y = sin ( x ) + 2

19. y = sin ( 2x )

20. y = 2 sin ( x )

21. y = cos x