Math: Advanced Math

SAT Question of the Day for October 10, 2026

The graphs of y=x2−6x+2y = x^2 - 6x + 2 and y=3x−16y = 3x - 16 intersect at two points. What is one of the intersection points?
  1. A.(3,−7)(3, -7)Correct answer
  2. B.(3,7)(3, 7)
  3. C.(6,−2)(6, -2)
  4. D.(6,16)(6, 16)

Explanation

The correct answer is (3,−7)(3, -7). Setting x2−6x+2=3x−16x^2 - 6x + 2 = 3x - 16 and simplifying yields x2−9x+18=0x^2 - 9x + 18 = 0, which factors as (x−3)(x−6)=0(x - 3)(x - 6) = 0. When x=3x = 3, y=3(3)−16=−7y = 3(3) - 16 = -7, giving the point (3,−7)(3, -7). When x=6x = 6, y=3(6)−16=2y = 3(6) - 16 = 2, giving (6,2)(6, 2). The point (3,7)(3, 7) uses the correct xx-value but has the wrong sign for yy. The point (6,−2)(6, -2) substitutes x=6x = 6 into the wrong expression. The point (6,16)(6, 16) miscomputes yy by evaluating 3(6)−163(6) - 16 incorrectly.

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