The graph of #y=x^2-6x+k# as its vertex on the x-axis. How do you find the value of k?

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Answer 1 · 2016-11-23T00:51:17

Set y = 0, evaluate the quadratic at #h = -b/(2a)# and solve for k.
#k = 9#

You want the to find the value of k such that the y coordinate of the vertex is 0.

#0 = x^2 - 6x + k#

The x coordinate, h, of the vertex is found, using the following equation:

#h = -b/(2a)#

#h = - -6/(2(1)) = 3#

Evaluate at x = 3:

#0 = 3^2 - 6(3) + k#

#k = 9#