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#1**+2 **

y = x^2 - 8x + 13

Let's put this in vertex form....complete the square on x

y = x^2 - 8x + 16 + 13 - 16 factor the first three terms....simplify the rest

y = (x -4)^2 - 3

The vertex of this parabola is (4, -3) .....it opens upward

Notice that the line that would be tangent to this parabola at the vertex would be the line y = -3 ⇒ "B"

So....this is the line that intersects the parabola in only one place

To get a feel for this look at the following graph : https://www.desmos.com/calculator/8gai6us8zr

Note that the other lines either intersect the graph twice....or not at all

CPhill Apr 23, 2018