Digital SAT Math Practice Question #1321
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Desmos slider: Graph both equations, add slider for $c$, and find the integer $c$ where the line is perfectly tangent to the parabola.
Set the equations equal to find intersection $x$-coordinates: $$x^2 - 6x + c = 2x - 1 \implies x^2 + (-8)x + (c + 1) = 0.$$ For the line and parabola to intersect at exactly one point, the discriminant must equal zero ($b^2 - 4ac = 0$): $$(...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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