Answer:
The correct option is 4.
Step-by-step explanation:
A function is called a quadratic function if the highest degree of the function is 2.
The simplified form of given functions are:
\(P(x)=2x(x^2+6)+1=2x^3+12x+1\)
The highest degree of the function is 3, therefore P(x) is not a quadratic function.
\(m(x)=-4(x+3)-2=-4x-12-2=-4x-14\)
The highest degree of the function is 1, therefore m(x) is not a quadratic function.
\(t(x)=-8x^2(x^2-6)+1=-8x^4+48x^2+1\)
The highest degree of the function is 4, therefore t(x) is not a quadratic function.
\(h(x)=3x(x-2)-4=3x^2-6x-4\)
The highest degree of the function is 2, therefore h(x) is a quadratic function. Option 4 is correct.
