Parabola Tangency & Constant k

For a positive constant k, the graph of the parabola intersects the given line at exactly one point. What is the value of k?

y = (x - 4)^2 + k \text{and} y = x - 2

Desmos 10-Second Shortcut

Desmos Slider Trick: Type y = (x - 4)^2 + k and y = x - 2 into Desmos. Add a slider for k (k > 0). Drag until the parabola touches the line at a single point (tangency), or equate and set discriminant b^2 - 4ac = 0.

Select Answer:

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