How do you write the quadratic in vertex form given #y=5x^2+5x-3#?

1 Answer
May 2, 2015

To be in vertex form a quadratic needs to be expressed as
#y=color(red)(m)(x-color(green)(a))^2+color(orange)(b)#
(where #(a,b)# is the vertex of the quadratic),

#y=5x^2+5x-3#

#y = color(red)(5)(x^2+x)-3 " extract the "color(red)( m)" term"#

#y = color(red)(5)(color(blue)(x^2+x+(1/2)^2) -(1/2)^2)-3 " "color(blue)("complete the square")#

#y=color(red)5(x+1/2)^2 - 5/4 -3#

#y=color(red)(5)(x- color(green)( (-1/2)))^2 + color(orange)(( -4 1/4))#