Question

The degree of the function f(x) = -(x + 1)2(2x - 3)(x + 2)2 is
. and its y-intercept is

Answer 1

Degree: 5

Y-intercept: 12

Explanation:

The given expression is

`f(x)=-(x+1)^2(2x-3)(x+2)^2`

Since the factors are multiplying, we can analyse the degree of each factor and add them to find the degree of the polynomial.

The degree of the factor
`-(x+1)^2` is 2.

The degree of
`(2x-3)` is 1

The degree of
`(x+2)^2` is 2

Therefore the degree of the polynomial is 2+1+2=5

To find the y-intercept, we put x=0.

`f(0)=-(0+1)^2(2(0)-3)(0+2)^2`

`f(0)=-(-3)(4)=12`

The y-intercept is 12