What is the vertex form of #y=23x^2-37x-29?

1 Answer
Jul 20, 2017

#y+4037/92=23(x-37/46)^2#

Explanation:

#y=23x^2-37x-29#

#=23(x^2-37/23x)-29#

#=23(x^2-37/23x)-29#

#=23(x^2-2xx37/46x+(37/46)^2)-23xx(37/46)^2-29#

#=23(x-37/46)^2-37^2/92-29#

#=23(x-37/46)^2-1369/92-29#

#=23(x-37/46)^2-4037/92#

or #y+4037/92=23(x-37/46)^2#

and vertex is #(37/46,-4037/92)# or #(37/46,-43 81/92)#

graph{23x^2-37x-29 [-2, 3, -50.7, 29.3]}

{Graph not to scale}