Digital SAT Math Practice Question #945
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Equate the two expressions for \( y \) to form a single quadratic equation \( Ax^2 + Bx + C = 0 \). Remember that having exactly one solution means the discriminant \( B^2 - 4AC \) must equal 0.
Desmos Shortcut: Enter the parabola in line 1: \( y = 3x^2 + (-12)x + 4 \). Enter line 2: \( y = 6x - k \) with a slider for \( k \). Move the slider until the line is perfectly tangent to the parabola at a single point.
To find when a quadratic and a line intersect at exactly one real point, set the two equations equal: \[ 3x^2 + (-12)x + 4 = 6x - k \] \[ 3x^2 + (-18)x + (4 + k) = 0 \] A quadratic equation has exactly one real solution if and only if its d...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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