Answer
First, make a vertical shrink of $y=x^2$ to obtain $y=\frac{1}{2}x^2$. Then, move the graph of $y=\frac{1}{2}x^2$ one unit down to obtain $k(x)=\frac{1}{2}x^2-1$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9cda1dd9-9753-4297-af28-be3d9b1f83bd/result_image/1562705874.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020516Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1f6559854496213c37a07b5adf0dfefd93868e8b4d5a1d563a81311bf30ea6ef)
Work Step by Step
Red: $y=x^2$
Green: $y=\frac{1}{2}x^2$
Blue: $k(x)=\frac{1}{2}x^2-1$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9cda1dd9-9753-4297-af28-be3d9b1f83bd/steps_image/small_1562705874.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020516Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1327eb9c448dd1e944ca7e09b27e3ee9605c9d39d2286e69a8744b268d1b9935)