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Quadratic Homework -- Graphing Quadratic Functions

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

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Summary: An introduction to graphing quadratic functions.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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} } } {}

Table 1
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(x−h)2+ky=a(x−h)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} } } {}

Table 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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