Please solve the Question below

Question

Write an equation that transforms y equals x to the 2nd power so that the graph is shifted 4 units left and 3 units down, faces down and is narrower.

Answer 1

The transformation for y = x² are:

y = a·(x-b)² + c

1. a = vertical stretch. Makes graph taller & narrower if a > 1, shorter and fatter if a < 1. Flips graph upside down if a < 0
2. b = horizontal shift. Right if b >0, left if b < 0
3. c = vertical shift. Up if a > 0, down if a < 0

Your instructions:

1. shifted 4 units left: b = -4
2. 3 units down: c = -3
3. faces down and is narrower: a = -2 (you can use any number less than -1)

y = a·(x-b)² - c

y = -2·(x-(-4))² + (-3) = -2·(x+4)² - 3