What is the vertex form of #y= 5x^2 + 9x − 4 #?

1 Answer
Feb 7, 2018

#y=5(x+9/10)^2-161/20#

Explanation:

Vertex form of equation for #y=ax^2+bx+c# is #y=a(x-h)^2+k# and vertex is #(h,k)#.

As #y=5x^2+9x-4#, we have

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

= #5(x^2+2xx9/10x+(9/10)^2-(9/10)^2)-4#

= #5((x+9/10)^2-5*(9/10)^2-4#

= #5(x+9/10)^2-81/20-4#

= #5(x+9/10)^2-161/20#

and as such vertex is #(-9/10,-161/20)# or #(-9/10,-8 1/10)#

graph{5x^2+9x-4 [-3.54, 1.46, -8.43, -5.93]}