Sketching Graphs

Sketching Graphs* Numbers on axes must be evenly spaced

Sketching Graphs* Numbers on axes must be evenly spaced

* y intercept occurs when x = 0

Sketching Graphs* Numbers on axes must be evenly spaced

* y intercept occurs when x = 0

* x intercept occurs when y = 0

Sketching Graphs* Numbers on axes must be evenly spaced

* y intercept occurs when x = 0

* x intercept occurs when y = 0

Once the intercepts have been found, curves are easy to sketch, if you know the basic shape.

Sketching Graphs* Numbers on axes must be evenly spaced

* y intercept occurs when x = 0

* x intercept occurs when y = 0

Once the intercepts have been found, curves are easy to sketch, if you know the basic shape.

If in doubt use a table of values and plot some points

Basic Curves

Basic Curvesxy

(1) Straight Linesy

x

Basic Curves

bmxy

xy (1) Straight Lines

y

x

Basic Curves

bmxy

xy 1̀power

(1) Straight Linesy

x 1̀power

Basic Curves

bmxy

xy 1̀power

(1) Straight Linesy

x 1̀power

(2) Parabolay

x

2xy

Basic Curves

bmxy

xy

cbxaxy 2

1̀power

(1) Straight Linesy

x 1̀power

(2) Parabolay

x

2xy

Basic Curves

bmxy

xy

cbxaxy 2

1̀power

(1) Straight Linesy

x 1̀power

(2) Parabolay

x

2xy 1̀power

2̀power

Basic Curves

bmxy

xy

cbxaxy 2

1̀power

0solve 2 cbxax

(1) Straight Linesy

x 1̀power

(2) Parabolay

x

2xy 1̀power

2̀power x intercepts:

Basic Curves

bmxy

xy

cbxaxy 2

1̀power

0solve 2 cbxax

(1) Straight Linesy

x 1̀power

(2) Parabolay

x

2xy 1̀power

2̀power x intercepts:

vertex: halfway between x intercepts

e.g. find the x intercepts and vertex of 342 xxy

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3y

x1 1,2

3

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3y

x1 1,2

3

(3) Cubic

y

x

3xy

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3y

x1 1,2

3

(3) Cubic

y

x

3xy dcxbxaxy 23

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3y

x1 1,2

3

(3) Cubic

y

x

3xy dcxbxaxy 23

1̀power

3̀power

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3y

x1 1,2

3

(3) Cubic

y

x

3xy dcxbxaxy 23

1̀power

3̀power

cubic.basicthelikelook it willthen

tofactorised becan it If 3kxay

e.g. find the x intercepts and vertex of 342 xxy 12 2 xy

1,2vertex 12 2 xx intercepts:

1212

x

x

x = 1 or x = 3y

x1 1,2

3

(3) Cubic

y

x

3xy dcxbxaxy 23

1̀power

3̀power

cubic.basicthelikelook it willthen

tofactorised becan it If 3kxay

Otherwise;y

x

(4) Higher Powersy

x

etc

even

6

4

xy

xy

(4) Higher Powersy

x

etc

even

6

4

xy

xy

y

x

etc

odd

7

5

xy

xy

(4) Higher Powersy

x

etc

even

6

4

xy

xy

y

x

etc

odd

7

5

xy

xy

As power gets bigger, curve gets; - flatter at base- steeper at the sides

(4) Higher Powersy

x

etc

even

6

4

xy

xy

y

x

etc

odd

7

5

xy

xy

As power gets bigger, curve gets; - flatter at base- steeper at the sides

(5) Hyperbolay

x

(4) Higher Powersy

x

etc

even

6

4

xy

xy

y

x

etc

odd

7

5

xy

xy

As power gets bigger, curve gets; - flatter at base- steeper at the sides

(5) Hyperbolay

x 1

1

xyOR

xy

(4) Higher Powersy

x

etc

even

6

4

xy

xy

y

x

etc

odd

7

5

xy

xy

As power gets bigger, curve gets; - flatter at base- steeper at the sides

(5) Hyperbolay

x 1

1

xyOR

xy

xy 1

one power on top of a fraction, one power on bottom of fraction

(6) Circley

x

222 ryx

r

r

-r

-r

(6) Circley

x

222 ryx 222 ryx

r

r

-r

-rboth power ‘2’coefficients are the same

(6) Circley

x

222 ryx

y

x

1

aay x

(7) Exponential

222 ryx

r

r

-r

-rboth power ‘2’coefficients are the same

1

(6) Circley

x

222 ryx

y

x

1

aay x

(7) Exponential

222 ryx

r

r

-r

-rboth power ‘2’coefficients are the same

xay

pronumeral in the power

1

(8) Rootsy

x

22 xry

r

r

-r

(8) Rootsy

x

22 xry y

x

xy

r

r

-r

(8) Rootsy

x

22 xry y

x

xy

r

r

-r

to tell what the curve looks like, square both sides

(8) Rootsy

x

22 xry y

x

xy

r

r

-r

to tell what the curve looks like, square both sides

circle

222

222

22

ryxxryxry

(8) Rootsy

x

22 xry y

x

xy

r

r

-r

to tell what the curve looks like, square both sides

circle

222

222

22

ryxxryxry

parabola

2

xyxy

(8) Rootsy

x

22 xry y

x

xy

r

r

-r

to tell what the curve looks like, square both sides

circle

222

222

22

ryxxryxry

parabola

2

xyxy

half topmeans

halfbottommeans

(8) Rootsy

x

22 xry y

x

xy

r

r

-r

to tell what the curve looks like, square both sides

circle

222

222

22

ryxxryxry

parabola

2

xyxy

half topmeans

halfbottommeans Exercise 2G; 1adeh, 2adgk, 3bdf, 5aeh, 7acegi, 8ad, 9a, 11c, 13acd,

15bd, 17*