Question

Does the parabola described by the function f(x)=3(x^(2)-2)-6x^(2)-(2+x^(2)) open upwards or downwards?

Answer 1

The parabola described by the function f(x) simplifies to -4x² - 8. Since the coefficient of the x² term is negative, the parabola opens downwards.

Step-by-step explanation:

The parabola described by the function f(x) = 3(x²- 2) - 6x² - (2 + x2) is determined to open upwards or downwards based on the coefficient of the x² term. First, we simplify the function:

f(x) = 3x² - 6 - 6x² - 2 - x²
f(x) = 3x² - 6x² - x² - 6 - 2
f(x) = -4x² - 8

After combining like terms, we have the x² coefficient as -4. Since the coefficient of the x² term is negative, the parabola opens downwards.