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 & Trig Graphs Quadratic Equations

Draw for -3 ≤ x ≤ 3

a) y = x2 + 3x – 4

b) y = 2x2 – 3x – 5

x -3 -2 -1 0 1 2 3

x2

3x

- 4

y

add

x -3 -2 -1 0 1 2 3

x2

-3x

- 5

y

add

x

x

y

y

Quadratic & Trig GraphsSolving Simultaneous Equations Graphically

Solve x2 + 5x – t = x + 2 simultaneously

y = x2 + 5x – tcurve

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.

Quadratic & Trig GraphsSolving Simultaneous Equations Graphically

Given the equations of a curve (original)

1. Check LHS is original Draw ‘y = RHS’

2. Change LHS to original

3. Draw ‘y = change’

yes

no

no

Quadratic & Trig GraphsSolving Simultaneous Equations Graphically

i) Draw for -2 ≤ x ≤ 5 the graph y = x2 – 3x – 3

ii) Use the graph to solve the equationsa) x2 – 3x – 3 = 0b) x2 – 3x – 3 = 4c) x2 – 3x + 1 = 0

x -2 -1 0 1 2 3 4 5

x2

-3x

- 3

yx

y

Quadratic & Trig GraphsSolving Simultaneous Equations Graphically

ii) Use the graph to solve the equationsa) x2 – 3x – 3 = 0b) x2 – 3x – 3 = 4c) x2 – 3x + 1 = 0

Check LHS is original

Draw ‘y = RHS’

Change LHS to original

Draw ‘y = change’

yes

no

no

x 0 30 60 90 120 150 180 210 240 270 300 330 360

sin x

Quadratic & Trig GraphsGraph of Trigonometrically

Functions

y = sin x

Use the above graph to solve

a) sin x = 0.5 b) sin x = -0.3

180 36090 2700

sin x

x 0 30 60 90 120 150 180 210 240 270 300 330 360

cos x

Quadratic & Trig GraphsGraph of Trigonometrically

Functions

y = cos x

180 36090 2700

cos x

x 0 30 60 90 120 150 180 210 240 270 300 330 360

tan x

Quadratic & Trig GraphsGraph of Trigonometrically

Functions

y = tan x

180 36090 2700

tan x

Quadratic & Trig Graphs Trig Graphs

Sketch basic trig graphs, know their key points and period

y = sin x

y = cos x

y = tan x

Period = 360°

-1 ≤ y ≤ 1

(90, 1)

(180, 0)

(270, -1)

(360, 0)(0, 0)

(0, 1)

(90, 0)

(180, -1)

(270, 0)

(360, 1)

Period = 360°

-1 ≤ y ≤ 1

Period = 180°

-∞ ≤ y ≤ ∞(0, 0)

(45, 1)

(180, 0)

(360, 0)

Quadratic & Trig Graphs Additional Notes

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.