If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting function g(x) in vertex form. a. f(x) = 1/2(x - 11)^2 - 5 b. f(x) = 1/2(x + 11)^2 - 5 c. f(x) = 2(x - 11)^2 - 5 d. f(x) = 2(x + 11)^2 - 5 if the parent function f(x) = x^2 is fatter translated 8 units to the right, then translated 1 unit down, write the resulting function g(x) in vertex form. a. g(x) = 1/3(x - 8)^2 - 1 b. g(x) = 1/3(x + 8)^2 - 1 c. g(x) = 3(x - 8)^2 - 1 d. g(x) = 3(x + 8)^2 - 1

The quadratic function given by:

is in vertex form. The graph of is a parabola whose axis is the vertical line and whose vertex is the point . So:

To translate the graph of a function to the right, left, upward or downward we have:

By knowing this things, we can solve our problem as follows:

FIRST.

Since the new function is fatter, the factor we need to multiply the term must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1