Question

5

State the translation T a.b required to obtain the graph with the first equation to that with the second equation.

a. y = 1/4 x² → y = 1/4x² - x + 2
b. y = 1/3 x³ → y = 1/3x³ - 3x² + 9x - 13
c. y = 2/x → y = (-3x + 14) / (x - 4)

Collin Li♦♦
6,305●1●4●13

asked Feb 28 at 2:14

Thao
181●2

Collin Li · Answer 1 · 2010-03-07 20:10:01Z UTC

a.
Here we have to complete the square: 1/4x² - x + 2 = 1/4(x² - 4x + 8) = 1/4(x-2)² + 1. From this form, now we can easily read the transformations.

b.
Here we have to try to get in the form a(x+b)³ + c, i.e.: "completing the cube".

1/3x³ - 3x² + 9x - 13
= 1/3(x³ - 9x² + 27x - 39)
= 1/3(x-3)³ - 4 (This step requires recognising a perfect cube)

Once again, now we can read the transformations easily.

c.
Here we have to use long division: (-3x + 14) / (x - 4) = -3 + 2/(x-4). Once again, from this form, now it is easy to read the transformations.

Steps 2 and 3 are:

Let me know if you need help with any of those steps.

Transformations required to obtain the graph

1 Answer