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Intersection of Curves and Lines occurs with … Two points One point No points or many Points!

Intersection of Curves and Lines Solve Simultaneously Show that y = 2x + 6 cuts the parabola y = x2 + 3 in 2 points. x2 + 3 = 2x + 6 x2 – 2x – 3 = 0 ∆ = (– 2)2 – 4 x 1 x (– 3) = 16 ∆ = a square number! Therefore 2 real-rational solutions.