Chapter 10 Quadratic Relations and Conic Sections

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Lesson 4-1 Graphing Quadratic Functions

Graph each function.

1. y = − x 2 y equals , negative , x squared
2. y = 1 3 x 2 y equals , 1 third , x squared
3. y = 2 x 2 + 5 y equals , 2 x squared , plus 5
4. y = x 2 + 6 x + 8 y equals , x squared , plus 6 x plus 8

Lesson 4-3 Identifying Quadratic Functions

Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms.

5. y = 6 x − x 2 + 1 y equals 6 x minus , x squared , plus 1
6. f ( x ) = − 2 ( 3 + x ) 2 + 2 x 2 f open x close equals negative 2 . open , 3 plus x , close squared . plus , 2 x squared
7. y = 2 x − y − 13 y equals 2 x minus y minus 13
8. y = 4 x ( 7 − 2 x ) y equals 4 x open 7 minus 2 x close
9. g ( x ) = − 2 x 2 − 3 ( x − 2 ) g open x close equals . negative 2 x squared . minus 3 open x minus 2 close
10. y = x − 2 ( x + 5 ) y equals x minus 2 open x plus 5 close

Lesson 4-6 Completing the Square

Complete the square.

11. x 2 + 8 x + □ x squared , plus 8 x plus white square
12. x 2 − 5 x + □ x squared , minus 5 x plus white square
13. x 2 + 14 x + □ x squared , plus 14 x plus white square

Rewrite each equation in vertex form. Then graph the function.

14. y = x 2 + 6 x + 7 y equals , x squared , plus 6 x plus 7
15. y = 2 x 2 − 4 x + 10 y equals , 2 x squared , minus 4 x plus 10
16. y = − 3 x 2 + x y equals negative 3 , x squared , plus x

Lesson 4-1 Graphing Quadratic Functions in Vertex Form

Graph each function.

17. y = 2 ( x − 3 ) 2 + 1 y equals 2 . open x minus 3 close squared . plus 1
18. y = − 1 ( x + 7 ) 2 − 4 y equals negative 1 . open x plus 7 close squared . minus 4

Lesson 2-7 Graphing Absolute Value Functions

Graph each function.

19. y = 2 | x | y equals 2 vertical line x vertical line
20. y = | x | + 2 y equals vertical line x vertical line plus 2

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