Final Answer:
The completed table values for the equation y=1/2x³ - 2x + 1 are as follows:
x y
-3 -13.5
-2 3
-1 2.5
0 1
1 -0.5
2 3
3 13.5
Step-by-step explanation:
To complete the table values for the given equation y=1/2x³ - 2x + 1, we need to substitute different values of x into the equation and solve for y. Starting with x=-3, we substitute this value into the equation: y=1/2(-3)³ - 2(-3) + 1.
This simplifies to y=-13.5. Similarly, for x=-2, we get y=3; for x=-1, y=2.5; for x=0, y=1; for x=1, y=-0.5; for x=2, y=3; and finally, for x=3, we get y=13.5.
By substituting these values of x into the equation and solving for y, we obtain the corresponding table values as shown above. The process involves plugging in each value of x into the equation and performing the necessary calculations to find the corresponding value of y.
This process allows us to generate a table of values that represent the relationship between x and y in the given equation, providing a clear understanding of how the equation behaves across different input values.