Question

question 8
consider the following polynomial.
q(x) = -3x² - 6x + 14
step 2 of 2: describe the behavior of the graph of q(x) as x → ±∞.
q(x) → as x → -∞
q(x) → as x → ∞

Explanation:

Step1: Identify Polynomial Degree and Leading Coefficient

The polynomial \( q(x) = -3x^2 - 6x + 14 \) is a quadratic (degree 2, even) with leading coefficient \( -3 \) (negative).

Step2: Analyze End Behavior for Even Degree

For even - degree polynomials, the end behavior (as \( x \to \pm\infty \)) depends on the leading coefficient. If the leading coefficient is negative, as \( x \to \infty \) and \( x \to -\infty \), the function values will both tend to \( -\infty \) because for large \( |x| \), the \( - 3x^2 \) term dominates. So when \( x\to-\infty \), \( q(x)\to-\infty \) and when \( x\to\infty \), \( q(x)\to-\infty \).

Answer:

As \( x\to-\infty \), \( q(x)\to\boxed{-\infty} \); as \( x\to\infty \), \( q(x)\to\boxed{-\infty} \)