SAT Math Practice Question #217 (Medium (635)) | Test Citadel
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SAT Math Difficulty: Medium (635)

Digital SAT Math Practice Question #217

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

The quadratic equation \( 2x^2 - 4x + c = 0 \) has exactly one real solution. What is the value of the constant \( c \)?
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Socratic AI Engine Step-by-Step Derivation
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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

Whenever an SAT question mentions the *number of solutions* a quadratic equation has, your brain should immediately scream 'Discriminant!' The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \). The discriminant is the part of...

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

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