Question

Which translation maps the graph of the function fx=x2 onto the function gx= x2+(-8x)+7

Answer 1

Shift the graph of f(x) 4 units to the right

and 7 units up

Explanation:

f(x) + n - shift a graph of f(x) n units up

f(x) - n - shift a graph of f(x) n units down

f(x + n) - shift a graph of f(x) n units to the left

f(x - n) - shift a graph of f(x) n units to the right

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We have

`f(x)=x^2,\ g(x)=x^2+(-8x)+7`

Convert the equation of g(x) to the vertex formula:

`y=a(x-h)^2+k`

`g(x)=x^2+(-8x)+7\\\\g(x0=x^2-2(x)(4)+7\\\\g(x)=\underbrace{x^2-2(x)(4)+4^2}-4^2+7\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\g(x)=(x-4)^2+7=f(x-4)+7\\\\\text{shift the graph of f(x) 4 units to the right and 7 units up}`