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

##### 1 Answer

Mar 22, 2016

#### Explanation:

The standard form of the quadratic function is :

# y = ax^2+bx+c# The function:

# y = 4x^2 + 5x + 2" is in this form " # with a = 4 , b = 5 and c = 2

>#"--------------------------------------------------"#

The vertex form of the quadratic function is

# y = a(x - h )^2 + k" (h,k) are the coords of vertex " # x-coord of vertex (h)

# = -b/(2a) = -5/(2xx4) = - 5/8 #

now substitute# x = -5/8 " into " y = 4x^2+5x+2 #

y-coord of vertex (k) =#4(-5/8)^2 + 5(-5/8 )+ 2 #

#= 4(25/64) - 25/8 + 2 = 7/16 #

hence vertex has coordinates# (-5/8 , 7/16 ) #

>#"------------------------------------------------"#

so a = 4 and (h , k )#= (-5/8 , 7/16 )#

# rArr" vertex form is " y = 4(x + 5/8)^2 + 7/16 #