Question

The function p is defined as p(x)=x2+4x-12

Part A
Write an expression that defines p(x-6)+5

Part B
Describe the transformations that map the graph of p(x) to p(x-6)+5. Justify your answer algebraically or by using key features of the graph.

Answer 1

Given the function
`p(x)=x^2+4x-12.`

Part A.

To write the expression that defines
`p(x-6)+5,` you have to substitute x-6 instead of x into the function expression and then add 5 to the function:

`p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.`

Part B.

1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).

2 transformation is translation 5 units up (+5 determines this transformation).