SAT Math Practice Question #327 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #327

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

In the xy-plane, the parabola \( y = -2x^2 + bx + c \) has its vertex at \( (h, k) \) and intersects the x-axis at \( x = -1 \) and \( x = 5 \). A line with equation \( y = mx + p \) passes through the vertex of the parabola and the point \( (0, -4) \). What is the value of \( m + p \)?
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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

Let's walk through this multi-step powerhouse of a geometry and algebra question! Step 1: Find the equation and vertex of the parabola. We are given the x-intercepts (roots) at \( x = -1 \) and \( x = 5 \), and the leading coefficient is -2...

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

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