Hello, jwebb19!

1.) For what value of the constant is the function continuous?

. .

To the left of , the graph is a parabola -- continuous.

To the right of , the graph is a straight line -- continuous.

The only discontinuity would be at .

To be a continuous function, the two curves must "meet" at

So we have: .

Therefore: .

2.) For what value of is the function continuous?

. .

The two branches of the function must be equal at

Hence: .

Therefore: .