Which function is the result of translating
f(x) = x² - 4x +3 with a vertical-stretch by a
factor of a and a reflection across the
y-axis?
a, y=-2x² - 8x +6
b.y = 2x² -8x + 6
c, y = 2x² + 8x+6
d, y=2x² +4x+6.

  C.  y = 2x² +8x +6

Step-by-step explanation:

Reflecting f(x) across the y-axis changes the sign of x, so the new function is ...

  f(-x)

Vertical scaling by a factor of "a" multiplies the function value by "a", so the new function is ...

  a·f(x)

Doing both gives you ...

 y = a·f(-x)

 y = ax² +4ax +3a

None of the answer choices look like this. However, they match this if a=2:

  y = 2x² +8x +6