Question

Describe the transformations of how the graph y=x^2 can be transformed into y= -1/5 (x-4)^2 + 2

Answer 1

Answer:

Reflected over the x-axis, vertically shrunk by a factor of 1/5, moved right 4 units and up 2 units.

Step-by-step explanation:

Parent Graph: f(x) = a(bx - h)² + k

a is vertical stretch (a > 1) or shrink (a < 1) and reflection over x-axis

b is horizontal stretch or shrink and reflection over y-axis

h is horizontal movement left (if positive) or right (if negative)

k is vertical movement up (if positive) or down (if negative)

Now that we have our rules, we simply apply it to y = -1/5(x - 4)² + 2

a = -1/5, so reflection over x-axis and vertical shrink of 1/5 (1/5 < 1)

Nothing has changed b, so no horizontal stretch/shrink

h = -4, so horizontal movement right 4 units

k = 2, so vertical movement up 2 units