graphing equations by type and with points by mr. barnard
TRANSCRIPT
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)