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"This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

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Collection by: Kenny M. Felder. E-mail the author

Module by: Kenny M. Felder. E-mail the author

Summary: An introduction to graphing quadratic functions.

## Exercise 1

Graph by plotting points. Make sure to include positive and negative values of xx size 12{x} {}!

y=x2y=x2 size 12{y=x rSup { size 8{2} } } {}

 x x size 12{x} {} y y size 12{y} {}

Note that there is a little point at the bottom of the graph. This point is called the “vertex.”

Graph each of the following by drawing these as variations of #1—that is, by seeing how the various numbers transform the graph of y = x 2 y = x 2 size 12{y=x rSup { size 8{2} } } {} . Next to each one, write down the coordinates of the vertex.

## Exercise 2

y = x 2 + 3 y = x 2 + 3 size 12{y=x rSup { size 8{2} } +3} {}

Vertex:

## Exercise 3

y = x 2 3 y = x 2 3 size 12{y=x rSup { size 8{2} } - 3} {}

Vertex:

## Exercise 4

y = ( x 5 ) 2 y = ( x 5 ) 2 size 12{y= $$x - 5$$ rSup { size 8{2} } } {}

Vertex:

## Exercise 5

Plot a few points to verify that your graph of #4 is correct.

## Exercise 6

y=(x+5)2y=(x+5)2 size 12{y= $$x+5$$ rSup { size 8{2} } } {}

Vertex:

## Exercise 7

y = 2x 2 y = 2x 2 size 12{y=2x rSup { size 8{2} } } {}

Vertex:

## Exercise 8

y=12x2y=12x2 size 12{y= { {1} over {2} } x rSup { size 8{2} } } {}

Vertex:

## Exercise 9

y = x 2 y = x 2 size 12{y= - x rSup { size 8{2} } } {}

Vertex:

In these graphs, each problem transforms the graph in several different ways.

## Exercise 10

y = ( x 5 ) 2 3 y = ( x 5 ) 2 3 size 12{y= $$x - 5$$ rSup { size 8{2} } - 3} {}

Vertex:

## Exercise 11

Make a graph on the calculator to verify that your graph of #10 is correct.

## Exercise 12

y = 2 ( x 5 ) 2 3 y = 2 ( x 5 ) 2 3 size 12{y=2 $$x - 5$$ rSup { size 8{2} } - 3} {}

Vertex:

## Exercise 13

y = 2 ( x 5 ) 2 3 y = 2 ( x 5 ) 2 3 size 12{y= - 2 $$x - 5$$ rSup { size 8{2} } - 3} {}

Vertex:

## Exercise 14

y = 1 2 ( x + 5 ) 2 + 3 y = 1 2 ( x + 5 ) 2 + 3 size 12{y= { {1} over {2} } $$x+5$$ rSup { size 8{2} } +3} {}

Vertex:

## Exercise 15

Where is the vertex of the general graph y=a(xh)2+ky=a(xh)2+k size 12{y=a $$x - h$$ rSup { size 8{2} } +k} {}?

## Exercise 16

Graph by plotting points. Make sure to include positive and negative values of yy size 12{y} {}! x=y2x=y2 size 12{x=y rSup { size 8{2} } } {}

 y y size 12{y} {} x x size 12{x} {}

Graph by drawing these as variations of #16—that is, by seeing how the various numbers transform the graph of x=y2x=y2 size 12{x=y rSup { size 8{2} } } {}.

## Exercise 17

x = y 2 + 4 x = y 2 + 4 size 12{x=y rSup { size 8{2} } +4} {}

## Exercise 18

x = ( y 2 ) 2 x = ( y 2 ) 2 size 12{x= $$y - 2$$ rSup { size 8{2} } } {}

## Exercise 19

Plot a few points to verify that your graph of #18 is correct.

## Exercise 20

x = y 2 x = y 2 size 12{x= - y rSup { size 8{2} } } {}

## Exercise 21

x = 2 ( y 2 ) 2 + 4 x = 2 ( y 2 ) 2 + 4 size 12{x= - 2 $$y - 2$$ rSup { size 8{2} } +4} {}

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