Question

What is the standard form of `y= (3x-2)(4x+1)-(4x-1)(2x-2)`?

Answer 1

"Smiling" Parabola
`(y=ax^2+bx+c)`

Explanation:

`y=(3x-2)(4x+1)-(4x-1)(2x-2)`
`=> y=12x^2-5x-2-(8x^2-10x+2)`
`=> y=12x^2-5x-2-8x^2+10x-2`
`=> y=4x^2-13x-4`

this is a form of:
`y=ax^2+bx+c`
when:
`a=4 , b=-13 , c=-4`

and therefore this function is a Parabola

(this is how it looks, "smiling"):
graph{4x^2-13x-4 [-3, 5, -20, 20]}