Final answer:
To find the zeros of a function, you set the function equal to zero and solve for x. We found the zeros for four different functions: y=(x+3)³ has a zero at -3; y=(x-4)² has a zero at 4; y=(2x+3)(x-1)² has zeros at -3/2 and 1. For y=2(x²)²-x, the equation is more complex and requires further expansion and factoring or the quadratic formula to find the zeros.
Step-by-step explanation:
To find the zeros of each function, we'll set the function equal to zero and solve for x.
For y=(x+3)³, set the equation to zero and solve:
0 = (x+3)³
x = -3
For y=2(x²)²-x, this equation is a bit more complex. You will need to expand the equation and use factoring or the quadratic formula to solve for the zeros.
For y=(x-4)², similarly, set the equation to zero:
0 = (x-4)²
x = 4
For y=(2x+3)(x-1)², we can find zeros by setting each factor to zero:
0 = 2x+3 and 0 = (x-1)²
x = -3/2, x = 1
Finding the zeros allows us to understand the points where the function intersects the x-axis.