Digital SAT Math Practice Question #1157
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Express the parabola in vertex form f(x) = a(x - h)^2 + k. Use the y-intercept to find 'a', then calculate the slope at x = 1.
Desmos Shortcut: Type y = 2(x - 3)^2 into Desmos. Then type y = -8x + 16 to observe the exact single point of tangency at (1, 8).
Since the vertex is at (3,0), the function is f(x) = a(x - 3)^2. Given f(0) = 18, a(0 - 3)^2 = 18 implies 9a = 18, so a = 2. Thus, f(x) = 2(x - 3)^2 = 2x^2 - 12x + 18. At x = 1, f(1) = 2(1 - 3)^2 = 8, so the point of tangency is (1, 8). The...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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