GRAPHING EQUATIONS BY TYPE AND WITH POINTS

By

Mr. Barnard

OBJECTIVE:

Know the shape of a graph from its equation and sketch a

graph by plotting points.

LIFE EXPECTANCY

AGE OF MOTHER WITH FIRST BORN

PROBABILITY OF FIRST MARRIAGE

BIRTHS TO UNMARRIED WOMEN

TYPES OF GRAPHS

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Linear: y = x

-5 -4 -3 -2 -1 1 2 3 4 5

-20

-10

10

20

x

y

Quadratic: y = x2

-5 -4 -3 -2 -1 1 2 3 4 5

-20

-10

10

20

x

y

Cubic: y = x3

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Square Root: xy

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Logarithms:

y= logx

y= lnx

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

y= sinx

y= cosx

Trigonometry:

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

y= tanx

y= cotx

Trigonometry:

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Trigonometry:

y= secx

y= cscx

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Absolute Value: y = |x|

COORDINATE PLANE

X-axis Y-axis

Quadrants

Origin

III

III IV

Ordered Pair

PRACTICE GRAPHING

USE YOUR WHITE BOARD, ERASER, AND MARKER

y = 5x - 2

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

y = 2x2 + 1

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

3xy

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

y = 3x3 – 2x2 - 1

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

y = 5sin2x

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

Plug in radian values for x!

INTERCEPTS

X-intercept

Y-intercept

Values where a line or curve crosses the x-axis. (y = 0)

Values where a line or curve crosses the y-axis. (x = 0)

Determine the x & y intercepts for: y = x2 - 1

y = x

y = 6x3 + 4x2

Which equation matches the graph?

y= 3x – 5 y= 2x2 – 5

y= 5x2 + 1

y= x3 - 5

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

SYMMETRY

The quality of having balance or exact parts of a figure on either side

of an axis.

EXAMPLES OF SYMMETRY

MORE EXAMPLES OF SYMMETRY

MORE EXAMPLES OF SYMMETRY

MORE EXAMPLES OF SYMMETRY

LOOK AROUND…SYMMETRY…

IT’S ALL AROUND YOU RIGHT NOW!

X-axis symmetry: can replace y with –y and produce the same equation.

Y-axis symmetry: can replace x with –x and produce the same equation.

Origin symmetry: can replace x with –x AND y with –y and produce the same equation.

TYPES OF SYMMETRY

Prove and disprove the type of symmetry for each:

y = x2 + 4

y = -x3 - 1

y = x4 - 2

Even function: symmetric with the y-axis

Odd function: symmetric with the origin

What type of function is symmetric with the x-axis?

Using y = x3 - x2, determine the x-intercepts (show evidence)y-intercepts (show evidence)type of symmetry (prove and disprove)graph (use intercepts, symmetry, &

other points

SKETCH A GRAPH:

Quadratic EquationX-axis SymmetryX-intercept at –2Y-intercept at 3

(3, 4)

SKETCH A GRAPH:

Quadratic EquationY-axis SymmetryX-intercept at 3Y-intercept at 2

(-5, -2)

SKETCH A GRAPH:

Cubic EquationOrigin SymmetryX-intercept at –4Y-intercept at 0

(-2, 2) and (-6, -4)

SUGGESTED PRACTICE:

Page 8 (1-12, 20, 32, 39-42, 44-47, 51, 54)

Page 8 (1-12, 20, 32, 39-42, 44-47, 51, 54)