Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?

You can find the second-degree polynomial function that has a leading coefficiente of 3 and roots - 4 and 6, in this way:

f(x) = 3 (x + 4) (x - 6)

Now expand the parenthesis using the notable product

f(x) = 3 (x^2 - 2x - 24)

Now use distributive property:

f(x) = 3x^2 - 6x - 72

As you see it has leading coefficient 3 and you can demonstrate that the roots are - 4 and 6.

f(x) = 3x^2 - 6x - 72