1. Quadratic and Trig Graphs
Learning Outcomes
Revise solution of quadratic equation.
Make tables of quadratic functions in order to make graphs.
Investigate quadratics graphs.
Given a series of equations and graphs, be able to match the correct equation with graph.
Be able to draw graphs of y = sinx, y = cosx, y = tanx and recognise important features.
Approx Time 8 – 10 periods

2. Quadratic Equations Quadratic & Trig Graphs Draw for -3 ≤ x ≤ 3 y
a) y = x2 + 3x – 4 x -3 -2 -1 1 2 3 x2 3x
- 4 y
add x y
b) y = 2x2 – 3x – 5 x -3 -2 -1 1 2 3 x2
-3x
- 5 y
add x

3. Solving Simultaneous Equations Graphically
Quadratic & Trig Graphs
Solving Simultaneous Equations Graphically
Solve x2 + 5x – t = x simultaneously
y = x2 + 5x – t
curve
y = x + 2 straight line
To solve these equations (graphically) we must draw the curve y= x2 + 5x and the line y = x + 2 and find the points of intersection.

4. Solving Simultaneous Equations Graphically
Quadratic & Trig Graphs
Solving Simultaneous Equations Graphically
Given the equations of a curve (original)
yes
1. Check LHS is original
Draw ‘y = RHS’ no
2. Change LHS to original no
3. Draw ‘y = change’

5. Solving Simultaneous Equations Graphically
Quadratic & Trig Graphs
Solving Simultaneous Equations Graphically
i) Draw for -2 ≤ x ≤ 5
the graph y = x2 – 3x – 3
ii) Use the graph to solve the equations
a) x2 – 3x – 3 = 0
b) x2 – 3x – 3 = 4
c) x2 – 3x + 1 = 0 y x -2 -1 1 2 3 4 5 x2
-3x
- 3 y x

6. Solving Simultaneous Equations Graphically
Quadratic & Trig Graphs
Solving Simultaneous Equations Graphically
ii) Use the graph to solve the equations
a) x2 – 3x – 3 = 0
b) x2 – 3x – 3 = 4
c) x2 – 3x + 1 = 0
Check LHS
is original
Draw
‘y = RHS’
Change LHS
to original
‘y = change’
yes no

7. Graph of Trigonometrically Functions
Quadratic & Trig Graphs
Graph of Trigonometrically Functions
y = sin x x 30 60 90
120
150
180
210
240
270
300
330
360
sin x
sin x 90
180
270
360
Use the above graph to solve
a) sin x = 0.5 b) sin x = -0.3

8. Graph of Trigonometrically Functions
Quadratic & Trig Graphs
Graph of Trigonometrically Functions
y = cos x x 30 60 90
120
150
180
210
240
270
300
330
360
cos x
cos x 90
180
270
360

9. Graph of Trigonometrically Functions
Quadratic & Trig Graphs
Graph of Trigonometrically Functions
y = tan x x 30 60 90
120
150
180
210
240
270
300
330
360
tan x
tan x 90
180
270
360

10. Trig Graphs Quadratic & Trig Graphs
Sketch basic trig graphs, know their key points and period
(90, 1)
Period = 360°
y = sin x
(0, 0)
(180, 0)
(360, 0)
-1 ≤ y ≤ 1
(270, -1)
(0, 1)
(360, 1)
y = cos x
Period = 360°
(90, 0)
(270, 0)
-1 ≤ y ≤ 1
(180, -1)
y = tan x
(45, 1)
Period = 180°
(360, 0)
(0, 0)
-∞ ≤ y ≤ ∞
(180, 0)

11. Quadratic & Trig Graphs
Additional Notes

12. At the end of the topic I will be able to
Quadratic and
Trig Graphs
Learning Outcomes:
At the end of the topic I will be able to
Can Revise
Do Further
Revise solution of quadratic equation.
Make tables of quadratic functions in order to make graphs.
Investigate quadratics graphs.
Given a series of equations and graphs, be able to match the correct equation with graph.
Be able to draw graphs of y = sinx, y = cosx, y = tanx and recognise important features.          