What is the vertex form of #y=x^2-5x+4 #?

1 Answer
Jim G.
Mar 2, 2016

#y = (x - 5/2 )^2 - 9/4 #

Explanation:

the standard form of a quadratic function is # ax^2 + bx + c #

the function #y = x^2 -5x + 4 " is in this form "#

by comparison: a = 1 , b = - 5 and c = 4

the vertex form of the function is # y = (x-h)^2 + k #

where (h,k) are the coords of the vertex.

x-coord (h) = #(-b)/(2a) = -(-5)/2 = 5/2 #

and y-coord ( k ) = #(5/2)^2 - 5(5/2) + 4 = -9/4 #

here ( h, k) = (#5/2 , -9/4 ") and " a = 1 #

#rArr y = (x - 5/2 )^2 - 9/4 " is the equation " #

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