Question

( y = 2x² - x ) is transformed by the following transformations in order: Horizontal shift -3, horizontal stretch 1/2, vertical stretch 2. Find the new function.

a) ( y = 2(x + 3)² - x )
b) ( y = 4(x + 3)² - x )
c) ( y = (x + 3)² - x )
d) ( y = (x - 3)² - x )

Answer 1

To find the new function, we need to apply horizontal and vertical transformations to the original function y = 2x² - x.

Step-by-step explanation:

Given the function y = 2x² - x, we need to apply the given transformations in order. Horizontal shift -3 means that we shift the graph 3 units to the left, so the equation becomes y = 2(x + 3)² - x.

Horizontal stretch 1/2 means that we compress the graph horizontally by a factor of 1/2, so the equation becomes y = 4(x + 3)² - x.

Vertical stretch 2 means that we elongate the graph vertically by a factor of 2, so the final equation is y = 4(x + 3)² - 2x.