Answer
First, reflect the graph of $y=x^2$ about the x-axis to obtain $y=-x^2$. Now, move $y=-x^2$ four units upwards to obtain $g(x)=4-x^2$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0a2f3237-e01f-42e0-98c8-0e4158328b9a/result_image/1562704023.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013852Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=89505e901a5cf0493fa573b4a5fc3829ca50de32877336c5c7256b6cd30442f4)
Work Step by Step
Red: $y=x^2$
Green: $y=-x^2$
Blue: $g(x)=4-x^2$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0a2f3237-e01f-42e0-98c8-0e4158328b9a/steps_image/small_1562704023.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013852Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=cb1cff82a03d0afdca9368335baba05eb1e3194a6eb59ef1940d072ad7cb5abd)
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