Question

The graph of y= (x^3) +6

is translated 4 units to the right.
The translated graph has equation y=f(x).
Work out f(x).

Give your answer in the form
x^3 + ax^2 + bx + c
where a, b and c are integers.

Answer 1

• f(x) = x³ - 12x² + 48x + 58

Explanation:

Given

• y = x³ + 6

Translating 4 units right

• x → x - 4
• f(x) = (x - 4)³ + 6
• f(x) = x³ - 3(x)²(4) + 3(x)(4)² - (4)³ + 6
• f(x) = x³ - 12x² + 48x - 64 + 6
• f(x) = x³ - 12x² + 48x + 58

Answer 2

`y=x^3-12x^2+48x-58`

Explanation:

Transformation Rules

`f(x+a)=f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a)=f(x) \: \textsf{translated}\:a\:\textsf{units right}`

Given equation:
`y=x^3+6`

If the graph of the equation is translated 4 units to the right, then we replace
`x` with
`(x-4)`:

`\implies y=(x-4)^3+6`

`\implies y=(x-4)(x-4)(x-4)+6`

`\implies y=(x-4)(x^2-8x+16)+6`

`\implies y=x^3-8x^2+16x-4x^2+32x-64+6`

`\implies y=x^3-12x^2+48x-58`