match each polynomial function to its graph.\n\n$f(x) = -x^2 + 6x - 14$\n$g(x) = x^3 - 12x^2 + 48x - 64$

Explanation:

Step1: Identify the degree of $f(x)$

The function $f(x) = -x^2 + 6x - 14$ is a quadratic function (degree 2).

Step2: Determine the shape of $f(x)$

A quadratic with a negative leading coefficient is a downward-opening parabola.

Step3: Identify the degree of $g(x)$

The function $g(x) = x^3 - 12x^2 + 48x - 64$ is a cubic function (degree 3).

Step4: Determine the shape of $g(x)$

A cubic function with a positive leading coefficient has an S-shape rising from left to right.

Step5: Match functions to graphs

The left graph is a downward parabola; the right graph is a cubic curve.

Answer:

The left graph matches $f(x) = -x^2 + 6x - 14$. The right graph matches $g(x) = x^3 - 12x^2 + 48x - 64$.