SAT Math Practice Question #1323 (Hard (760)) | Test Citadel
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SAT Math Difficulty: Hard (760)

Digital SAT Math Practice Question #1323

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

In the $xy$-plane, the graph of the parabola $y = x^2 - 2x + c$ intersects the line $y = 4x - 10$ at exactly one point. What is the value of the constant $c$?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Desmos slider: Graph both equations, add slider for $c$, and find the integer $c$ where the line is perfectly tangent to the parabola.

Masterclass Solution & Distractor Trap Analysis

Set the equations equal to find intersection $x$-coordinates: $$x^2 - 2x + c = 4x - 10 \implies x^2 + (-6)x + (c + 10) = 0.$$ For the line and parabola to intersect at exactly one point, the discriminant must equal zero ($b^2 - 4ac = 0$): $...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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