What is the vertex of # y= x^2- 6x + 14 #?

1 Answer
Ken C.
Jan 31, 2016

(3, 5)

Explanation:

The x-coordinate of the vertex of a parabola is given by #-b/(2a)#. Remember that parabolas in standard form are #ax^2+bx+c#. With this in mind, we can see that, for our parabola, #a = 1#, #b = -6#, and #c = 14#.

To find the x-coordinate of the vertex, we just plug in the value of #a# and #b# into #-b/(2a)#:

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

Now that we have the #x#, we plug it into our parabola to find #y#:

#(3)^2-6(3)+14 = 9-18+14 = 5#

Our y-coordinate is 5, meaning our vertex is the point (3,5).

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