SAT Math Practice Question #566 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #566

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

In the \(xy\)-plane, a parabola with equation \( y = ax^2 + bx + c \) passes through the points \( (-1, 0) \), \( (0, -6) \), and \( (3, 0) \). A second parabola is defined by the equation \( y = -ax^2 + bx - c \). What is the \( y \)-coordinate of the vertex of the second parabola?
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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 is an elite-level algebra problem that tests your ability to rapidly construct polynomial equations from roots and then apply transformations. Step 1: Construct the first parabola. We are given the \(x\)-intercepts (roots): \( (-1, 0) ...

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

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