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.

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

[tex]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.[/tex]

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).

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.

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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.