Answer
a) The red line is $2x^2-8$, and the blue line is the other function.
b) $2x^2-8$, after factoring out a $2$, is the same function as $4x^2-4$.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/22f63cff-380b-43f3-b5e8-de0a52159162/result_image/1534626207.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013724Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=fbd2791ce44172cfebabf7ff795afc76ea5d71f28d39d0877a41c22afa15a09e)
Work Step by Step
Please see the graphs.
$x^2-4=0$
$x^2-4+4=0+4$
$x^2 =4$
$\sqrt {x^2} = \sqrt 4$
$x=2, -2$
$2x^2-8=0$
$x^2-8+8=0+8$
$2x^2 =8$
$2x^2/2 =8/2$
$x^2 = 4$
$\sqrt {x^2} = \sqrt 4$
$x=2, -2$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/22f63cff-380b-43f3-b5e8-de0a52159162/steps_image/small_1534626207.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013724Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=5fb4dde978708d542f0ba0b205e178ae4ac7227fc5b3204c07f97cdc4d843d93)