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

##### 1 Answer

Mar 2, 2016

#### 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 " #