16Hit1600
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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