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Homework: Graphing Quadratic Functions II

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

Summary: Some more homework problems on graphing quadratic functions.

Put each equation in the form y=a(x−h)2+ky=a(x−h)2+k size 12{y=a \( x - h \) rSup { size 8{2} } +k} {} or x=a(y−k)2+hx=a(y−k)2+h size 12{x=a \( y - k \) rSup { size 8{2} } +h} {}, and graph.

Exercise 1

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

Exercise 2

y = x 2 + 6x + 5 y = x 2 + 6x + 5 size 12{y=x rSup { size 8{2} } +6x+5} {}

Exercise 3

Plot at least three points to verify your answer to #2.

Exercise 4

y = x 2 − 8x + 16 y = x 2 − 8x + 16 size 12{y=x rSup { size 8{2} } - 8x+"16"} {}

Exercise 5

y = x 2 − 7 y = x 2 − 7 size 12{y=x rSup { size 8{2} } - 7} {}

Exercise 6

y + x 2 = 6x + 3 y + x 2 = 6x + 3 size 12{y+x rSup { size 8{2} } =6x+3} {}

Exercise 7

Use a graph on the calculator to verify your answer to #6.

Exercise 8

y + x 2 = x 2 + 6x + 9 y + x 2 = x 2 + 6x + 9 size 12{y+x rSup { size 8{2} } =x rSup { size 8{2} } +6x+9} {}

Exercise 9

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

Exercise 10

x = 3y 2 + 6y x = 3y 2 + 6y size 12{x=3y rSup { size 8{2} } +6y} {}

Exercise 11

x 2 + y 2 = 9 x 2 + y 2 = 9 size 12{x rSup { size 8{2} } +y rSup { size 8{2} } =9} {}

Exercise 12

Explain in words how you can look at any equation, in any form, and tell if it will graph as a parabola or not.

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