Which quadratic rule represents the data in the table?
x -1 0 1 2 3
y 6 5 6 9 14
y = -2x²+5
y = x²+5
y = x²-5
y = x²+5
The quadratic rule that represents the data in the table is: y = x²+5.
To find the quadratic rule that represents the data in the table, we can substitute the values of x and y into each of the given equations to see which one matches the data.
Substituting the values of x and y from the table into the first equation y = -2x² + 5:
For x = -1, y = -2(-1)² + 5 = -2 + 5 = 3
For x = 0, y = -2(0)² + 5 = 0 + 5 = 5
For x = 1, y = -2(1)² + 5 = -2 + 5 = 3
For x = 2, y = -2(2)² + 5 = -8 + 5 = -3
For x = 3, y = -2(3)² + 5 = -18 + 5 = -13
Substituting the values of x and y from the table into the second equation y = x² + 5:
For x = -1, y = (-1)² + 5 = 1 + 5 = 6
For x = 0, y = (0)² + 5 = 0 + 5 = 5
For x = 1, y = (1)² + 5 = 1 + 5 = 6
For x = 2, y = (2)² + 5 = 4 + 5 = 9
For x = 3, y = (3)² + 5 = 9 + 5 = 14
Comparing the calculated values with the given data in the table, we can see that the second equation y = x² + 5 accurately represents the data. Therefore, the quadratic rule that represents the data in the table is y = x² + 5.