GRAPHING EQUATIONS BY TYPE AND WITH POINTS By Mr. Barnard.

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Presentation 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

Linear: y = x

Quadratic: y = x 2

Cubic: y = x 3

Square Root:

Logarithms: y= logx y= lnx

y= sinx y= cosx Trigonometry:

y= tanx y= cotx Trigonometry:

y= secx y= cscx

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

y = 2x 2 + 1

y = 3x 3 – 2x 2 - 1

y = 5sin2x 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 = x  y = x  y = 6x 3 + 4x 2

Which equation matches the graph? y= 3x – 5 y= 2x 2 – 5 y= 5x y= x3 x3 - 5

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

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 = x  y = -x  y = x 4 - 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 = x 3 - x 2, 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 Equation X-axis Symmetry X-intercept at –2 Y-intercept at 3 (3, 4)

SKETCH A GRAPH: Quadratic Equation Y-axis Symmetry X-intercept at 3 Y-intercept at 2 (-5, -2)

SKETCH A GRAPH: Cubic Equation Origin Symmetry X-intercept at –4 Y-intercept at 0 (-2, 2) and (-6, -4)

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