Transcript Slide 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.
Quadratic Equations
Quadratic & Trig Graphs
Draw for -3 ≤ x ≤ 3
a) y =
x
x2
y
+ 3x – 4
-3
-2
-1
0
1
2
3
x2
x
add 3x
-4
y
y
b) y = 2x2 – 3x – 5
x
-3
-2
-1
0
1
2
3
x2
add -3x
-5
y
x
Quadratic & Trig Graphs
Solve
Solving Simultaneous
Equations Graphically
x2 + 5x – t = x + 2
y = x2 + 5x – t
curve
simultaneously
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.
Solving Simultaneous
Equations Graphically
Quadratic & Trig Graphs
Given the equations of a curve (original)
1. Check LHS is original
no
2. Change LHS to original
no
3. Draw ‘y = change’
yes
Draw ‘y = RHS’
Solving Simultaneous
Equations Graphically
Quadratic & Trig Graphs
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
0
1
2
3
4
5
x2
-3x
-3
y
x
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
Draw
‘y = RHS’
yes
Check LHS
is original
no
Change LHS
to original
no
Draw
‘y = change’
Quadratic & Trig Graphs
Graph of Trigonometrically
Functions
y = sin x
x
0
30
60
90
120
150
180 210
sin x
sin x
0
90
180
270
360
Use the above graph to solve
a) sin x = 0.5
b) sin x = -0.3
240
270
300
330 360
Quadratic & Trig Graphs
Graph of Trigonometrically
Functions
y = cos x
x
0
30
60
90
120
150
180 210
240
cos x
cos x
0
90
180
270
360
270
300
330 360
Quadratic & Trig Graphs
Graph of Trigonometrically
Functions
y = tan x
x
0
30
60
90
120
150
180 210
240
270
tan x
tan x
0
90
180
270
360
300
330 360
Trig Graphs
Quadratic & Trig Graphs
Sketch basic trig graphs, know their key points and period
(90, 1)
y = sin x
Period = 360°
(180, 0)
(0, 0)
(360, 0)
-1 ≤ y ≤ 1
(270, -1)
(360, 1)
(0, 1)
y = cos x
Period = 360°
(90, 0)
(270, 0)
-1 ≤ y ≤ 1
(180, -1)
y = tan x
(45, 1)
(360, 0)
(0, 0)
(180, 0)
Period = 180°
-∞ ≤ y ≤ ∞
Quadratic & Trig Graphs
Additional Notes
Quadratic and
Trig Graphs
Learning Outcomes:
At the end of the topic I will be able to





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.
Can
Do
Revise
Further
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