The quadratic $4x^2+2x-1$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What

Question

The quadratic $4x^2+2x-1$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?

GPT-5 mini · Answer

Complete the square:

4x^2+2x-1 = 4[x^2 + (1/2)x] -1
= 4[(x+1/4)^2 - 1/16] -1
= 4(x+1/4)^2 -1/4 -1
= 4(x+1/4)^2 -5/4.

So a=4, b=1/4, c=-5/4 and a+b+c = 4 + 1/4 -5/4 = 3.

The quadratic $4x^2+2x-1$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?