Question

find g(x), where g(x) is the translation 10 units left and 4 units up of f(x) = x². write your answer in the form a(x - h)² + k, where a, h, and k are integers. g(x) =

Explanation:

Step1: Recall translation rules

For a function \( y = f(x) \), translating \( h \) units left replaces \( x \) with \( x + h \), and translating \( k \) units up adds \( k \) to the function. The vertex form is \( a(x - h)^2 + k \), where \( (h,k) \) is the vertex.

Step2: Apply horizontal translation

\( f(x)=x^2 \) translated 10 units left: replace \( x \) with \( x + 10 \), so we get \( (x + 10)^2 \).

Step3: Apply vertical translation

Translate 4 units up: add 4 to the function. So \( g(x)=(x + 10)^2+4 \). In vertex form \( a(x - h)^2 + k \), \( a = 1 \), \( h=-10 \) (since \( x - (-10)=x + 10 \)), and \( k = 4 \).

Answer:

\( g(x)=(x + 10)^2 + 4 \) (or in the form \( 1(x - (-10))^2 + 4 \))