Problem

Analyze \(y=x^{2}+4\) and \(y=-2x+1\) for real intersections. Preserve the line’s signs during substitution, compute the discriminant, and connect the classification to the displayed answer graph.

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set equal=x²+4=-2x+1; reduced=x²+2x+3=0; discriminant=2²+4·1·3=16>0; classification=two real intersections; graph meaning=line crosses parabola twice

set equal=x²+4=-2x+1; reduced=x²+2x+3=0; discriminant=2²−4·1·3=-8<0; classification=no real solution; graph meaning=line and parabola have no real intersection

set equal=x²+4=-2x+1; reduced=x²−2x+3=0; discriminant=(-2)²−4·1·3=-8<0; classification=no real solution; graph meaning=line and parabola do not intersect

set equal=x²+4=-2x+1; reduced=x²+2x+3=0; discriminant=-8; claimed roots=x=-1±sqrt(2); classification=two real intersections; graph meaning=line crosses parabola twice

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Analyze \(y=x^{2}+4\) and \(y=-2x+1\) for real intersections. Preserve the line’s signs during substitution, compute the discriminant, and connect the classification to the displayed answer graph.

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