What is #y= x ^ { 2} - 10x - 2# in vertex form?

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Answer 1 · 2017-08-01T20:10:37

#y = (x-5)^2-27" [4]"#

The given equation is in the standard form of a parabola that opens up or down:

#y = ax^2+bx+c" [1]"#

where #a = 1, b = -10, and c = -2#

The vertex form of the same type is:

#y = a(x-h)^2+k" [2]"#

where "a" is the same value as the standard form and #(h,k)# is the vertex.

Substitute the value for "a" into equation [2]:

#y = (x-h)^2+k" [3]"#

The formula for h is:

#h = -b/(2a)#

Substituting in the known values:

#h = -(-10)/(2(1))#

#h = 5#

Substitute the value for h into equation [3]:

#y = (x-5)^2+k" [3]"#

The value of k can be found by evaluating the original equation at the value for h:

#k = 5^2-10(5)-2#

#k = 25-50-2#

#k = -27#

#y = (x-5)^2-27" [4]"#