For what values of m does the line y = mx - 5 not intersect the parabola y = x^2 + 3x + 4?
Answer and explanation
Correct answer: C. -3 < m < 9
- Step 1: Step 1: Set equations equal: x^2 + 3x + 4 = mx - 5 => x^2 + (3 - m)x + 9 = 0. For no intersection, Delta < 0. Step 2. Step 2: Delta = (3 - m)^2 - 4(1)(9) = (3 - m)^2 - 36 < 0 => (3 - m)^2 < 36 => -6 < 3 - m < 6. Subtract 3: -9 < -m < 3 => -3 < m < 9. Answer: -3 < m < 9. Why not the others: Delta > 0 gives two intersection points; Delta = 0 gives a tangent line.
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