SAT Math Practice Question #1276 (Hard (780)) | Test Citadel
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SAT Math Difficulty: Hard (780)

Digital SAT Math Practice Question #1276

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

In the $xy$-plane, the graphs of $y = 2x^2 - 8x + c$ and $y = 4x - 11$ intersect at exactly one point. What is the value of the constant $c$?
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Socratic AI Engine Step-by-Step Derivation
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⚡ 15-Second Desmos Speed Hack

Desmos hack: Type $y = 2x^2 - 8x + c$ and $y = 4x - 11$ into Desmos. Add a slider for $c$. Slide $c$ until the parabola is perfectly tangent to the line. At $c = 7$, they touch at exactly $(3, 1)$.

Masterclass Solution & Distractor Trap Analysis

Set the two equations equal to find their intersection points: $$2x^2 - 8x + c = 4x - 11 \implies 2x^2 - 12x + (c + 11) = 0.$$ For the graphs to intersect at exactly one point, this quadratic equation must have a discriminant of zero ($b^2 ...

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

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