Question

find g(x), where g(x) is the translation 3 units left 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 horizontal translation rule

For a left shift by $c$ units, replace $x$ with $x+c$ in $f(x)$.

Step2: Apply shift to $f(x)=x^2$

Substitute $x$ with $x+3$: $g(x)=(x+3)^2$

Step3: Rewrite in vertex form

Rewrite $(x+3)^2$ as $1(x - (-3))^2 + 0$ to match $a(x-h)^2+k$.

Answer:

$1(x - (-3))^2 + 0$ or simplified as $(x+3)^2$