Parabola Tangent

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We start with the graph of the parabola y = x² and a line drawn from the point (–1, –2) tangent to the parabola. Find the slope of the line.

Hmm. Surely this is a calculus problem and this is grade 11. What’s up? Well, this is actually an interesting problem which makes nice use of the quadratic formula. To get the students started we suggest that they consider the family of all lines drawn from the point (–1, –2). Among all those lines, what property identifies the tangent line?