Answer:
To fill out the table, we need to plug in each value of x into the equation y = 3x² + 4 and evaluate the expression to find the corresponding value of y.
x | y
--|--
-3| 31
-1| 7
0 | 4
1 | 7
B | 7
-2| A
7 | 148
From the table, we can see that:
- When x = -3, y = 3(-3)² + 4 = 31
- When x = -1, y = 3(-1)² + 4 = 7
- When x = 0, y = 3(0)² + 4 = 4
- When x = 1, y = 3(1)² + 4 = 7
- When x = B, y = 7
- When x = -2, y = 3(-2)² + 4 = A
- When x = 7, y = 3(7)² + 4 = 148
To find the values of A and B, we can use the information from the table:
- When x = -2, y = A, so we know that 3(-2)² + 4 = A. Simplifying this expression, we get A = 16.
- When x = B, y = 7, so we know that 3B² + 4 = 7. Subtracting 4 from both sides and dividing by 3, we get B² = 1. Therefore, B = ±1. However, we also know that y = 7 when x = 1, so B must be equal to 1.
Therefore, the completed table of values is:
x | y
--|--
-3| 31
-1| 7
0 | 4
1 | 7
1 | 7
-2| 16
7 | 148