SAT Math Practice Question #346 (Hard (800)) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #346

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

In the \( xy \)-plane, the equations for a parabola and a line are given by the system below: \[ y = x^2 - 4x + c \] \[ y = mx + 2 \] The system of equations above has exactly one real solution. If \( m \) and \( c \) are positive integers, what is the minimum possible value of \( c \)?
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

First, we are dealing with a system of equations consisting of a parabola and a line. To find their intersection points, we set the equations equal to each other: \[ x^2 - 4x + c = mx + 2 \] Now, let's move everything to one side to form a ...

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.