Let P(x) = 4x^3 - 2x^2 + 7x - 1, and let Q(x) = P(x)^2. What is the y-intercept of Q(x)?

Q(x) = [P(x)]²     and     P(x)  =  4x³ - 2x² + 7x - 1

--->     Q(x)  =  [ 4x³ - 2x² + 7x - 1 ]²

 

The y-intercept occurs when the x-value is 0; so to find the y-intercept of Q(x) substitute 0 for x:

--->     Q(0)  =  [ 4(0)³ - 2(0)² + 7(0) - 1 ]²

                      =  [ 0 - 0 + 0 - 1 ]²

                    =  [ -1 ]²

                    =  1

 

So, the y-intercept occurs at (0, 1)