Download presentation

Presentation is loading. Please wait.

Published byLarissa Lees Modified over 3 years ago

2
An equation for which the graph is a line

3
Any ordered pair of numbers that makes a linear equation true. (9,0) IS ONE SOLUTION FOR Y = X - 9

4
Example: y = x + 3

5
Step 1: ~ Three Point Method ~ Choose 3 values for x

6
Step 2: Find solutions using table y = x + 3 Y | X 0 1 2

7
Step 3: Graph the points from the table (0,3) (1,4) (2,5)

8
Step 4: Draw a line to connect them

9
Graph using a table (3 point method) 1) y = x + 3 2) y = x - 4

10
Where the line crosses the x- axis

11
The x-intercept has a y coordinate of ZERO

12
To find the x- intercept, plug in ZERO for y and solve

13
Describes the steepness of a line

14
Equal to: Rise Run

15
The change vertically, the change in y

16
The change horizontally or the change in x

17
Step 1: Find 2 points on a line (2, 3) (5, 4) (x 1, y 1 ) (x 2, y 2 )

18
Step 2: Find the RISE between these 2 points Y 2 - Y 1 = 4 - 3 = 1

19
Step 3: Find the RUN between these 2 points X 2 - X 1 = 5 - 2 = 3

20
Step 4: Write the RISE over RUN as a ratio Y 2 - Y 1 = 1 X 2 - X 1 3

21
Where the line crosses the y- axis

22
The y-intercept has an x- coordinate of ZERO

23
To find the y- intercept, plug in ZERO for x and solve

24
y = mx + b m = slope b = y-intercept

25
Mark a point on the y- intercept

26
Define slope as a fraction...

27
(RISE)

28
Denominator is the horizontal change (RUN)

29
Graph at least 3 points and connect the dots

30
Definitions 3 forms for a quad. function Steps for graphing each form Examples Changing between eqn. forms

31
A function of the form y=ax 2 +bx+c where a0 making a u-shaped graph called a parabola. Example quadratic equation:

32
The lowest or highest point of a parabola. Vertex Axis of symmetry- The vertical line through the vertex of the parabola. Axis of Symmetry

33
y=ax 2 + bx + c If a is positive, u opens up If a is negative, u opens down The x-coordinate of the vertex is at To find the y-coordinate of the vertex, plug the x- coordinate into the given eqn. The axis of symmetry is the vertical line x= Choose 2 x-values on either side of the vertex x- coordinate. Use the eqn to find the corresponding y-values. Graph and label the 5 points and axis of symmetry on a coordinate plane. Connect the points with a smooth curve.

34
a=2 Since a is positive the parabola will open up. Vertex: use b=-8 and a=2 Vertex is: (2,-2) Axis of symmetry is the vertical line x=2 Table of values for other points: x yTable of values for other points: x y 06 06 10 10 2-2 2-2 30 30 46 46 * Graph! x=2

36
(-1,10) (-2,6) (2,10) (3,6) X =.5 (.5,12)

37
y=a(x-h) 2 +k If a is positive, parabola opens up If a is negative, parabola opens down. The vertex is the point (h,k). The axis of symmetry is the vertical line x=h. Dont forget about 2 points on either side of the vertex! (5 points total!)

38
y=2(x-1) 2 +3 Open up or down? Vertex? Axis of symmetry? Table of values with 5 points?

39
a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Table of values x y -1 2 -2 3.5 -3 4 -4 3.5 -5 2 Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

40
(-1, 11) (0,5) (1,3) (2,5) (3,11) X = 1

41
y=a(x-p)(x-q) The x-intercepts are the points (p,0) and (q,0). The axis of symmetry is the vertical line x= The x-coordinate of the vertex is To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. If a is positive, parabola opens up If a is negative, parabola opens down.

42
Since a is negative, parabola opens down. The x-intercepts are (-2,0) and (4,0) To find the x-coord. of the vertex, use To find the y-coord., plug 1 in for x. Vertex (1,9) The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex)The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex) x=1 (-2,0)(4,0) (1,9)

43
y=2(x-3)(x+1) Open up or down? X-intercepts? Vertex? Axis of symmetry?

44
(-1,0)(3,0) (1,-8) x=1

45
The key is to FOIL! (first, outside, inside, last) Ex: y=-(x+4)(x-9)Ex: y=3(x-1) 2 +8 =-(x 2 -9x+4x-36) =3(x-1)(x-1)+8 =-(x 2 -5x-36) =3(x 2 -x-x+1)+8 y=-x 2 +5x+36 =3(x 2 -2x+1)+8 =3x 2 -6x+3+8 y=3x 2 -6x+11

Similar presentations

OK

CC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non‐vertical line in the coordinate plane; derive.

CC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non‐vertical line in the coordinate plane; derive.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on conservation of environmental resources Ppt on structure of atom class 11th Ppt on op amp circuits applications Ppt on water activity symbol Ppt on artificial intelligence system Ppt on video conferencing project Ppt on active and passive voice Ppt on revolution of the earth and seasons kids Ppt on formation of day and night Ppt on famous wildlife sanctuaries in india