Question

1. function g is a transformation of the parent function f(x) = x². the graph of g is a translation left 4 units and down 2 units of the graph of f. write the equation for g in the form y = a(x - h)² + k. a y = 2(x + 2)² + 2 b y = 2(x - 2)² + 4 c y = (x + 4)² - 2 d y = (x - 4)² - 2

Explanation:

Step1: Recall Transformation Rules

For a function \( y = f(x) \), a horizontal translation left \( h \) units is \( y = f(x + h) \), and a vertical translation down \( k \) units is \( y = f(x) - k \). The parent function is \( f(x)=x^2 \), so \( a = 1 \) (no vertical stretch/compression).

Step2: Apply Horizontal Translation

Translation left 4 units: Replace \( x \) with \( x + 4 \) in \( f(x) \), so \( f(x + 4)=(x + 4)^2 \).

Step3: Apply Vertical Translation

Translation down 2 units: Subtract 2 from the function, so \( g(x)=(x + 4)^2-2 \).

Step4: Match with Options

The equation \( y=(x + 4)^2-2 \) corresponds to option C.

Answer:

C. \( y = (x+4)^2 - 2 \)