Question

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

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).