SAT Math Practice Question #257 (Hard (710)) | Test Citadel
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SAT Math Difficulty: Hard (710)

Digital SAT Math Practice Question #257

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

The equation \( y = -3x^2 + bx + c \) represents a parabola in the \(xy\)-plane, where \( b \) and \( c \) are constants. If the vertex of the parabola is at the point \( (4, 20) \), what is the \( y \)-intercept of the parabola?
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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

This is a fantastic Advanced Math problem because it tests your fluency with the vertex form of a quadratic equation. Let's walk through it together. The standard form is given as \( y = -3x^2 + bx + c \). From this, we immediately know tha...

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

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