SAT Math Practice Question #208 (Medium (620)) | Test Citadel
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SAT Math Difficulty: Medium (620)

Digital SAT Math Practice Question #208

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

The equation \( y = -2x^2 + 12x - 10 \) is graphed in the \( xy \)-plane. What is the \( y \)-coordinate of the vertex 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

Let's find the peak of this parabola! Finding the vertex of a quadratic equation is an essential SAT skill. The equation is given in standard form: \( y = ax^2 + bx + c \), where \( a = -2 \), \( b = 12 \), and \( c = -10 \). Step 1: Find t...

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

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