Question

Let the graph of g be a translation 3 units up, followed by a vertical stretch by a factor of 2 and a reflection in the x-

Answer 1

Answer:

The answer is $g(x)= -6x(x-1)+3$

Step-by-step explanation:

we know that f(x) is written as $3x^{2}-3x$

to show that the graph is being translated up, vertically stretching, and reflecting across the x axis, we need to factor the function.

$f(x)= 3x^{2}-3x \\ 3x(x-1)$

now we can incorporate the changes to this graph.

multiply 3x by 2 and -1. (2 for a stretch and -1 for a reflection).

$-6x(x-1)$

tack on the +3 to show a translation of 3 units up.

$-6x(x-1)+3$

therefore, $g(x)= -6x(x-1)+3$

hope this helps!