SAT Math Practice Question #1321 (Hard (760)) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Hard (760)

Digital SAT Math Practice Question #1321

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 $y = x^2 - 6x + c$ intersects the line $y = 2x - 1$ at exactly one point. What is the value of the constant $c$?
Select Your Answer:
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: $$x^2 - 6x + c = 2x - 1 \implies x^2 + (-8)x + (c + 1) = 0.$$ 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...

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.