B Apply

22. Think About a Plan An ellipse has center (3, 2), one vertex (9, 2), and one co-vertex ( 3 , − 1 ) . open 3 comma negative 1 close .  Sketch its graph. Then write its equation.
    • How can the sketch help you write the equation?
    • What information do you need to write the equation?
23. Reasoning Use the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 eh x squared , plus b x y plus , c y squared , plus d x plus e y plus f equals 0  to identify the shape of the graph that results in each case.
    1. A = C = D = E = 0 , B ≠ 0 , F ≠ 0 eh equals c equals d equals e equals 0 comma b not equal to 0 comma f not equal to 0
    2. A = B = C = D = 0 , E ≠ 0 , F ≠ 0 eh equals b equals c equals d equals 0 comma e not equal to 0 comma f not equal to 0

Sketch each conic section. Then write its equation.

24. A parabola has vertex ( 2 , − 3 ) open 2 comma negative 3 close  and focus (2, 5).
25. A hyperbola has center ( 6 , − 3 ) , open 6 comma negative 3 close comma  one focus (6, 0), and one vertex ( 6 , − 1 ) . open 6 comma negative 1 close .
26. Theater Arts The director of a stage show asks you to design an elliptical platform. Her sketch shows the platform centered at (9, 7) from the front left corner of the stage. The platform has a 12-ft major axis parallel to the front edge of the stage and extends to within 3 ft of the edge. Write an equation that models the platform.

Write an equation for each graph.

The graph of each equation is to be translated 2 units left and 4 units up. Write each new equation.

29. ( x − 2 ) 2 + ( y + 4 ) 2 = 16 open x minus 2 close squared . plus . open y plus 4 close squared . equals 16
30. ( x − 3 ) 2 64 + ( y − 3 ) 2 36 = 1 fraction open , x minus 3 , close squared , over 64 end fraction . plus . fraction open , y minus 3 , close squared , over 36 end fraction . equals 1
31. y = 2 x 2 y equals , 2 x squared
32. 9 x 2 + 3 x + 10 = 16 y 2 + 154 + 3 x 9 , x squared , plus 3 x plus 10 equals , 16 y squared , plus 154 plus 3 x

Graph each pair of functions. Identify the conic section represented by the graph and write the functions as a single equation in standard form.

33. y = 36 − 4 x 2 y = − 36 − 4 x 2 table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals . square root of 36 minus 4 , x squared end root , row2 column 1 , y , column 2 equals negative . square root of 36 minus 4 , x squared end root , end table
34. y = 4 x 2 − 36 y = − 4 x 2 − 36 table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals . square root of 4 , x squared , minus 36 end root , row2 column 1 , y , column 2 equals negative . square root of 4 , x squared , minus 36 end root , end table
35. y = 0.5 36 − x 2 y = − 0.5 36 − x 2 table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals 0.5 . square root of 36 minus , x squared end root , row2 column 1 , y , column 2 equals negative 0.5 . square root of 36 minus , x squared end root , end table

C Challenge

36. Open-Ended On a graphing calculator, create a design using three translated quadratic relations.

Table of Contents