the parent function of a quadratic equation is vertically stretched by a factor of 2, then translated 5 units to the right and 1 unit down. write the equation of the new function in vertex form

A vertical stretch appears as a multiplier for the function value. Translation right appears as a value subtracted from the independent variable. Translation up appears as a value added to the function value.

For function f (x), stretching by a factor of 2, then translation 5 right and - 1 up will give the function

... g (x) = 2f (x-5) - 1

When f (x) = x², this becomes ...

... g (x) = 2 (x - 5) ² - 1

... g (x) = 2x² - 20x + 49