Which quadratic rule represents the data in the table?
x: -1 | 0 | 1 | 2 | 3
Y: 4 | 5 | 4 | 1 | -4
A. y= -2x^2 + 5
B. y= -x^2 + 5
C. y= x^2 - 4
D. y= x^2 + 5
Is it A or C?
It is D
To determine which quadratic rule represents the data in the table, we can substitute the values of x and y into each equation and see which equation matches the given values.
Let's evaluate the options:
A. y = -2x^2 + 5
When x is -1, y = -2(-1)^2 + 5 = -2 + 5 = 3 (not 4)
When x is 0, y = -2(0)^2 + 5 = 0 + 5 = 5 (correct)
When x is 1, y = -2(1)^2 + 5 = -2 + 5 = 3 (not 4)
When x is 2, y = -2(2)^2 + 5 = -8 + 5 = -3 (not 1)
When x is 3, y = -2(3)^2 + 5 = -18 + 5 = -13 (not -4)
B. y = -x^2 + 5
When x is -1, y = -(-1)^2 + 5 = -1 + 5 = 4 (correct)
When x is 0, y = -(0)^2 + 5 = 0 + 5 = 5 (correct)
When x is 1, y = -(1)^2 + 5 = -1 + 5 = 4 (correct)
When x is 2, y = -(2)^2 + 5 = -4 + 5 = 1 (correct)
When x is 3, y = -(3)^2 + 5 = -9 + 5 = -4 (correct)
C. y = x^2 - 4
When x is -1, y = (-1)^2 - 4 = 1 - 4 = -3 (not 4)
When x is 0, y = (0)^2 - 4 = 0 - 4 = -4 (correct)
When x is 1, y = (1)^2 - 4 = 1 - 4 = -3 (not 4)
When x is 2, y = (2)^2 - 4 = 4 - 4 = 0 (not 1)
When x is 3, y = (3)^2 - 4 = 9 - 4 = 5 (not -4)
Therefore, the correct quadratic rule representing the data in the table is B. y = -x^2 + 5.
To determine which quadratic rule represents the data in the table, we can compare the given values of x and y with the equation options.
Option A: y = -2x^2 + 5
Substituting the given values of x into this equation:
For x = -1: y = -2(-1)^2 + 5 = -2 + 5 = 3 (not equal to the corresponding y value in the table)
For x = 0: y = -2(0)^2 + 5 = 5 (not equal to the corresponding y value in the table)
For x = 1: y = -2(1)^2 + 5 = -2 + 5 = 3 (not equal to the corresponding y value in the table)
For x = 2: y = -2(2)^2 + 5 = -8 + 5 = -3 (not equal to the corresponding y value in the table)
For x = 3: y = -2(3)^2 + 5 = -18 + 5 = -13 (not equal to the corresponding y value in the table)
Option C: y = x^2 - 4
Substituting the given values of x into this equation:
For x = -1: y = (-1)^2 - 4 = 1 - 4 = -3 (not equal to the corresponding y value in the table)
For x = 0: y = (0)^2 - 4 = 0 - 4 = -4 (equal to the corresponding y value in the table)
For x = 1: y = (1)^2 - 4 = 1 - 4 = -3 (equal to the corresponding y value in the table)
For x = 2: y = (2)^2 - 4 = 4 - 4 = 0 (not equal to the corresponding y value in the table)
For x = 3: y = (3)^2 - 4 = 9 - 4 = 5 (not equal to the corresponding y value in the table)
Comparing the values, we can see that option B: y = -x^2 + 5 aligns with the data in the table, as it produces the correct y values for all given x values.
Therefore, the correct answer is option B.