Question

If you apply the changes below to the quadratic parent function, f(x) = x2, what is the equation of the new function? Shift 3 units right. Vertically stretch by a factor of 4. Reflect over the x-axis. A. g(x) = (–4x – 3)2 B. g(x) = –4(x – 3)2 C. g(x) = 4x2 + 3 D. g(x) = –4(x + 3)2

Answer 1

To apply the changes to the equation of a vertical stretch of 4 and a translation of 3 units to the right, as well as the correct answer would be choice B.

The reason for this is when you apply a vertical stretch, because it changes the y-values (which causes it to vertically stretch or appear skinnier when graphed), you would multiply 4 to f(x) which would look like 4x^2.

Then, since you have a reflection over the x-axis, you must multiply a -1 to f(x) to reflect it over the x-axis which would result in -4x^2.

Finally, it also asks to shift the graph right 3 which by moving it right, you change the x values meaning you will perform f(x-3) to achieve this (subtract the value from x when you move right, and add the value to x when you move left).

This therefore results in your answer, the new graph would be
g(x)= -4(x-3)^2 or choice B.