SAT Math Practice Question #320 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #320

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

The quadratic function \( f \) is defined by \( f(x) = -2x^2 + 12x - 14 \). The function \( g \) is defined by \( g(x) = f(x - c) + d \), where \( c \) and \( d \) are constants. The graph of \( y = g(x) \) in the \( xy \)-plane has a maximum value of \( 18 \), and its \( y \)-intercept is \( 0 \). Which of the following could be the value of \( c \)?
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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

This incredibly deep algebra question tests your knowledge of vertex form, function transformations, and strategic algebraic solving. Let's conquer it step-by-step. Step 1: Find the vertex of the original function \( f(x) \). We need to con...

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

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