Question

How are the graphs of f(x) = x^2 and g(x) = -(x + 2)^2 - 4 related?

Answer 1

Answer: g(x) is shifted left 2 units, down 4 units, and reflected over the x-axis.

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k     where

• a is the vertical stretch
• -a is a reflection over the x-axis
• (h, k) is the vertex
• --> h is the horizontal shift (positive is RIGHT, negative is LEFT)
• --> k is the vertical shift (positive is UP, negative is DOWN)

f(x) = x²

g(x) = -(x + 2)² - 4

         a = -1     reflected over the x-axis

         h = -2    shifted left 2 units

         k = -4     shifted 4 units down

Answer 2

Answer:

g(x) is shifted left 2 units, down 4 units, and reflected over the x-axis.

Step-by-step explanation: