Advanced MathVery hardConstant making a line tangent to a parabola
Advanced Math practice question
For what value of c is the line y = x + c tangent to the parabola y = x²?
Answer: -0.25 or -1/4
x² = x + c gives x² − x − c = 0, which has one solution when 1 + 4c = 0, so c = −1/4.
Common wrong answers
- If you answered 0
- 0 gives two intersections, at x = 0 and x = 1.
- If you answered 1
- 1 gives two intersections.
- If you answered 0.25
- 0.25 has the sign wrong.
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