graphing equations by type and with points by mr. barnard
TRANSCRIPT
![Page 1: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/1.jpg)
GRAPHING EQUATIONS BY TYPE AND WITH POINTS
By
Mr. Barnard
![Page 2: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/2.jpg)
OBJECTIVE:
Know the shape of a graph from its equation and sketch a
graph by plotting points.
![Page 3: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/3.jpg)
LIFE EXPECTANCY
![Page 4: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/4.jpg)
AGE OF MOTHER WITH FIRST BORN
![Page 5: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/5.jpg)
PROBABILITY OF FIRST MARRIAGE
![Page 6: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/6.jpg)
BIRTHS TO UNMARRIED WOMEN
![Page 7: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/7.jpg)
TYPES OF GRAPHS
![Page 8: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/8.jpg)
-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
![Page 9: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/9.jpg)
-5 -4 -3 -2 -1 1 2 3 4 5
-20
-10
10
20
x
y
Quadratic: y = x2
![Page 10: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/10.jpg)
-5 -4 -3 -2 -1 1 2 3 4 5
-20
-10
10
20
x
y
Cubic: y = x3
![Page 11: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/11.jpg)
-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
![Page 12: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/12.jpg)
-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
![Page 13: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/13.jpg)
-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:
![Page 14: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/14.jpg)
-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:
![Page 15: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/15.jpg)
-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
![Page 16: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/16.jpg)
-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|
![Page 17: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/17.jpg)
COORDINATE PLANE
![Page 18: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/18.jpg)
X-axis Y-axis
Quadrants
Origin
III
III IV
Ordered Pair
![Page 19: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/19.jpg)
PRACTICE GRAPHING
USE YOUR WHITE BOARD, ERASER, AND MARKER
![Page 20: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/20.jpg)
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
![Page 21: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/21.jpg)
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
![Page 22: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/22.jpg)
3xy
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
![Page 23: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/23.jpg)
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
![Page 24: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/24.jpg)
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!
![Page 25: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/25.jpg)
INTERCEPTS
![Page 26: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/26.jpg)
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)
![Page 27: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/27.jpg)
Determine the x & y intercepts for: y = x2 - 1
y = x
y = 6x3 + 4x2
![Page 28: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/28.jpg)
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
![Page 29: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/29.jpg)
SYMMETRY
The quality of having balance or exact parts of a figure on either side
of an axis.
![Page 30: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/30.jpg)
EXAMPLES OF SYMMETRY
![Page 31: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/31.jpg)
MORE EXAMPLES OF SYMMETRY
![Page 32: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/32.jpg)
MORE EXAMPLES OF SYMMETRY
![Page 33: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/33.jpg)
MORE EXAMPLES OF SYMMETRY
![Page 34: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/34.jpg)
LOOK AROUND…SYMMETRY…
IT’S ALL AROUND YOU RIGHT NOW!
![Page 35: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/35.jpg)
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
![Page 36: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/36.jpg)
Prove and disprove the type of symmetry for each:
y = x2 + 4
y = -x3 - 1
y = x4 - 2
![Page 37: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/37.jpg)
Even function: symmetric with the y-axis
Odd function: symmetric with the origin
What type of function is symmetric with the x-axis?
![Page 38: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/38.jpg)
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
![Page 39: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/39.jpg)
SKETCH A GRAPH:
Quadratic EquationX-axis SymmetryX-intercept at –2Y-intercept at 3
(3, 4)
![Page 40: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/40.jpg)
SKETCH A GRAPH:
Quadratic EquationY-axis SymmetryX-intercept at 3Y-intercept at 2
(-5, -2)
![Page 41: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/41.jpg)
SKETCH A GRAPH:
Cubic EquationOrigin SymmetryX-intercept at –4Y-intercept at 0
(-2, 2) and (-6, -4)
![Page 42: GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard](https://reader038.vdocuments.net/reader038/viewer/2022103122/56649cf45503460f949c1b1f/html5/thumbnails/42.jpg)
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)