Question

What is the vertex of for the parabola y = x2 - 2kx + 6? k is a constant that is not zero. Write your answer as an ordered pair in terms of k.

Answer 1

Okay, remember that the x-coordinate of a parabola is given by x = -b/2a. After we find x, we are going to substitute it into the equation and solve for the y-coordinate. Let's do it:

x=-(-2k)/2(1)=2k/2=1k=k

Replacing x=1 in the equation:

y=(k)²-2k(k)+6=k²-2k²+6=-k²+6

Finally we obtain the following ordered pair: (k, -k²+6)