Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s) the degree of the function f(x) = -(x+1)^2(2x-3)(x+2)^2 is _ , and its y-intercept is ( _ , _ )

Answer 1

Degree of the function = 5

y-intercept = (0, 12)

Explanation:

Degree of a polynomial function is determined by the degree of the term having highest degree.

In the given function,

f(x) = -(x + 1)²(2x - 3)(x + 2)²

(x + 1)² → highest degree term = x²

(2x - 3) → highest degree term = x

(x + 2)² → highest degree term = x²

When we multiply these terms,

(x + 1)²(2x - 3)(x + 2)² highest degree term of the function will be,

`x^(2) * x * x^(2) = x^(5)`

Therefore, degree of the function = 5

For y-intercept,

f(0) = -(0 + 1)²(0 - 3)(0 + 2)² = 12

Therefore, y-intercept of the function is (0, 12)