Which function is a quadratic function? a p(x) = 2x(x2 + 6) + 1 b m(x) = –4(x + 3) – 2 c t(x) = –8x2(x2 – 6) + 1 d h(x) = 3x(x – 2) – 4?

For a quadratic function, the highest order of x is 2.

a.
p(x) = 2x(x² + 6) + 1
p(x) = 2x³ + 12x + 1
The highest order of x is 3, so that p(x) is not a quadric function.

b.
m(x) = -(4x + 3) - 2
m(x) = -4x - 3 - 2
m(x) = -4x - 5
The highest order of x is 1, so that m(x) is not a quadric function.

c.
t(x) = –8x²(x² – 6)
t(x) = –8x⁴ + 48x²
The highest order of x is 4, so that t(x) is not a quadric function.

d.
h(x) = 3x(x – 2) – 4
h(x) = 3x² – 6x – 4
The highest order of x is 2, so that t(x) is not a quadric function.

The answer: d. h(x) = 3x(x – 2) – 4

h(x) = 3x(x – 2) – 4

A quadratic function is of degree 2.