Question

Given the characteristics of a function, what is its equation?

a) y = 2x^3 - 7x^2 + 4x - 6
b) y = -6x + 2
c) y = (x - 3)(x + 1)
d) y = 2(x - 3)(x + 1)

Answer 1

The equation that matches the given characteristics is y = 2(x - 3)(x + 1).

Step-by-step explanation:

Given the characteristics of a function, we need to determine which option's equation matches the given characteristics. Let's analyze each option:

a) y = 2x^3 - 7x^2 + 4x - 6: This is a cubic function with a degree of 3.

b) y = -6x + 2: This is a linear function with a slope of -6.

c) y = (x - 3)(x + 1): This is a quadratic function with a degree of 2 and a vertex at (1, -2).

d) y = 2(x - 3)(x + 1): This is a quadratic function with a degree of 2 and a vertex at (2, -4).

Based on the given characteristics, the option that corresponds to the function is option d) y = 2(x - 3)(x + 1).