Analyze \(x^{2}-4x+4=0\) by naming \(a\), \(b\), and \(c\), computing the discriminant, and translating a zero result into the correct repeated-root and tangent-intersection classification.

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a = 1, b = −4, c = 4; D = 0; zero; 2 distinct real x-values; two intersections.

a = 1, b = −4, c = 4; D = 16 + 16 = 32; positive; 2 real x-values; two intersections.

a = 1, b = −4, c = 4; D = 0; positive; 2 real x-values; two intersections.

a = 1, b = −4, c = 4; D = 16 − 16 = 0; zero; 1 repeated real x-value; one tangent intersection.

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Curriculum context

Course: Math II
Standard: A-REI.7
Category: Algebra
Domain: Reasoning with Equations and Inequalities
Objective: Solve simple linear-quadratic systems algebraically and graphically.
Problem type: Interpret line-parabola intersections in context