Final answer:
Upon simplification, the function y=(x + 4)(6x + 3) - 6x² becomes y = 27x + 12, which is a linear equation since the x² terms cancel out. There is no quadratic term, the linear term is 27x, and the constant term is 12.
Step-by-step explanation:
To determine whether the function y=(x + 4)(6x + 3) - 6x² is linear or quadratic, we need to simplify the equation. By expanding the brackets, we get y = 6x² + 3x + 24x + 12 - 6x². Simplifying further, the 6x² terms cancel each other out, leaving us with y = 3x + 24x + 12. Combining like terms, we get y = 27x + 12, which is a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.
The function has no quadratic term since the x² terms were eliminated through simplification. Therefore, there is no quadratic term, the linear term is 27x and the constant term is 12. This places the function in the family of linear equations rather than quadratics.