Help me Solve these algebra problems?

Question

Determine whether each function is linear or quadtatic. Identify the quadratic, linear, and constant terms.

y= x+4

y= 3x(x-2)

f(x)= (3x)(2x) + 6

f(x)= -x(2x+8)

Answer 1

The first thing you need to do is multiply out all of the terms to see the highest degree term in the equation. Then you need to know the definitions of linear and quadratic equations.

y = x + 4 is clearly linear

y = 3x(x - 2) = 3x^2 - 6x is quadratic

f(x) = (3x)(2x) + 6 = 6x^2 + 6 is quadratic

f(x) = -x(2x+8) = -2x^2 - 8x is quadratic

The terms containing x^2 are the quadratic terms, the terms containing simple a single power of x is the linear terms, and the terms without any x are the constant terms.