on the real number line and on cartesian coordinates presented by: vicki angel and jan whisonant...

Post on 01-Jan-2016

212 Views

Category:

Documents

0 Downloads

Preview:

Click to see full reader

TRANSCRIPT

GRAPHING

onThe Real Number Line

and onCartesian Coordinates

Presented by:Vicki Angel and Jan WhisonantTransitions Math ConferenceAustin, TXMay 6-7, 2011

OBJECTIVE

The participants will learn strategies for teaching graphing of equations and

inequalities in one and two variables.

Points, intervals, lines, and parabolas will be included.

Copyright © 2008 Texas Education Agency Copyright © Notice.  The materials are copyrighted © and trademarked ™ as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions:• Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from TEA.• Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA.• Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way. No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged.• Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside t the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty.

For information contact Richard Jarrell Office of Copyrights, Trademarks, License Agreements, and Royalties Texas Education Agency 1701 N. Congress Ave. Austin, TX 78701-1494 (512) 463-9270 or (512) 936-6060

For each real number there corresponds exactly

one point on the real number line and for each

point on the real number line there corresponds

exactly one real number.

X = -2

Solution to an equation in one unknown

X < 2

Solution to an inequality in one unknown

x ≤ -2 or x ≥ 1

Solution of a compound inequality

-3 ≤ x ≤ 4

Solution of a compound inequality

Linear Equations

Standard Form

ax + by + c = 0

Slope- Intercept Form

y = mx + b

m = slope b = y intercept

Graphing Methodsfor Linear Equations

1. Find both the x and y intercepts2. Use the y intercept and the slope3. Use a T chart, selecting values for x and then finding the values of y for each x

Graphing using Intercepts

y = - 4x + 8

If x = 0, then y = 8y = -4(0) + 8y = 0 + 8 = 8

If y = 0, then x = 20 = - 4x + 84x = 8, x = 2

Graphing using the slope and y intercept

y = 5/4 x – 2

y intercept = - 2

slope = 5/4

Graphing using T Chart

y = 3/2 x + 3

x y

0 3

2 6

- 4 - 3

Linear Inequalities 1. Graph the inequality by replacing the

inequality with an = sign and graph the line just like it was an equation…using any of the three methods we discussed

2. If the inequity is < or > make the line a dotted line.

3. Use a test point to determine which side of the line to shade.

Using a Test Point

Select a point that is not on the line. Substitute the x and y values of the point

into the inequality. If those values make the inequality true,

then shade the side of the line that the point is on.

If those values make the inequality false, then shade the opposite side of the line from the selected point.

y ≤ - 8/3 x + 2

y intercept = 2

slope = - 8/3

y > 6x + 4

y intercept = 4

slope = 6/1

Graphing a quadratic equation

Find the vertex and at least two other points on the graph, then use the axis of symmetry to add two more points to the graph.

When the equation is in the form

The vertex is (h , k) and the line of symmetry is x = h

)0(a )( 2 khxay

y = x²

x y

0 0

2 4

- 3 9

Vertex (3,4) Line of symmetry: x=3

x y

4

1

2

- 4

4 )32(- 2 xy

Vertex: (1, -5) Line of symmetry: x=1

7

-2

3

0

x y

2 - 6 - 3 2 xxy

x

- 4 1

y

- 1

1 6

- 2

y ≥ (x+2)² - 3

top related