Question

Use the description to write the quadratic function in vertex form.

The parent function f(x) = x² is reflected across the x-axis, vertically compressed by a factor of 2, and translated 3 unit(s) right to create g.
What is the function?

Answer 1

The function g(x) after applying the given transformations to f(x) = x² is g(x) = -½ (x-3)².

Step-by-step explanation:

The function g(x) represents a transformation of the parent function f(x) = x². To find g(x), we need to reflect the parent function across the x-axis, compress it vertically by a factor of 2, and then translate it 3 units to the right. Reflecting f(x) across the x-axis multiplies the function by -1, which makes it -x². The vertical compression by a factor of 2 means we multiply -x² by ½, which gives us -½ x². Finally, translating the function 3 units to the right replaces x with (x-3), resulting in -½ (x-3)². Therefore, the transformed function g(x) in vertex form is g(x) = -½ (x-3)².