Math help. Translation of an equation...?

Question

ok, so here is the Question im stuck on.... "the graph of the function f(x)= 2x^3 - 3x^2 +x +1 is translated to its image, g(x), by the vector [1, -1]. Write g(x) in the form g(x)= ax^3 + bx^2 + cx +d "

ok, so basically you need to translate f(x)= 2x^3 - 3x^2 +x +1 to the right one unit and down one unit.... i dont know how to do this for a polynomial of third degree... can anyone please show me how... thanx alot...

Answer 1

Hi,

To move the equation one to the right, replace each x by (x - 1) and simplify the equation:

2(x-1)³ -3(x-1)² + (x-1) + 1 =

2(x³ - 3x² + 3x - 1) - 3(x² - 2x + 1) + x - 1 + 1 =

2x³ - 6x² + 6x - 2 - 3x² + 6x - 3 + x - 1 + 1 =

2x³ -9x² + 13x - 5

So f(x) = 2x³ -9x² + 13x - 5 is the equation when it is moved one square to the right. When it is moved down one, that makes every point on the graph one square lower by subtracting one more off of the constant at the end. The equation moved one right and down one is:

f(x) = 2x³ -9x² + 13x - 5 - 1 more OR f(x) = 2x³ -9x² + 13x - 6

f(x) = 2x³ -9x² + 13x - 6 is your answer.

The original graph The new graph
------------------------- ----------------------
x......y.........................x.....y
0.....1.........................1....0
1.....1.........................2....0
2.....7.........................3....6
3...31.........................4..30

I hope that helps!!

Answer 2

Replace x by (x-1) in f(x) and expand out; combine like powers of x, and then finally add (-1) to the result (to move down 1 unit).

You should get g(x) = 2x^3 - 9x^2 + 13x - 6