Final answer:
Upon simplification, the function y - (x + 4)(6x + 3) - 6x^2 is quadratic because it includes an x² term. It simplifies to y = -12x² - 27x - 12, with -12x² being the quadratic term, -27x the linear component, and -12 the constant term.
Step-by-step explanation:
The given function y - (x + 4)(6x + 3) - 6x^2 needs to be simplified to determine whether it is a linear or quadratic function.
To simplify, first expand the brackets: y - (6x² + 24x + 3x + 12) - 6x².
This simplifies to y - (6x² + 27x + 12) - 6x², and further to y - 6x² - 27x - 12 - 6x².
Combining like terms, we get y - 12x² - 27x - 12.
As there is an x² term, the function is not linear, it is indeed a quadratic function.
The coefficients of x² and x indicate the quadratic and linear components, while the constant term is -12.
Therefore, in y = 12x² + 27x + 12, the quadratic term is 12x², the linear term is 27x, and the constant term is 12.