Which equation is true for all the ordered pairs in the table?
X Y
0 0
1 4
2 16
3 36
A. Y=4x^2
B.Y=1/4x^2
C.Y=16x^2
D. 1/16x^2
well, x^2 gives
0 0
1 1
2 4
3 9
so, what do you think?
To determine the correct equation for all the ordered pairs in the table, we'll look for a pattern in the values of x and y.
Let's examine the values of y for each value of x:
- When x = 0, y = 0
- When x = 1, y = 4
- When x = 2, y = 16
- When x = 3, y = 36
We can see that the value of y is increasing as x increases, and the values of y seem to be related to the square of x.
Now, let's check the options provided:
A. Y = 4x^2
Plugging in the values from the table:
For x = 0, 4x^2 = 4(0)^2 = 0 (not correct)
For x = 1, 4x^2 = 4(1)^2 = 4 (not correct)
For x = 2, 4x^2 = 4(2)^2 = 16 (not correct)
For x = 3, 4x^2 = 4(3)^2 = 36 (not correct)
B. Y = 1/4x^2
Plugging in the values from the table:
For x = 0, 1/4x^2 = 1/4(0)^2 = 0 (not correct)
For x = 1, 1/4x^2 = 1/4(1)^2 = 1/4 (not correct)
For x = 2, 1/4x^2 = 1/4(2)^2 = 1/4 (not correct)
For x = 3, 1/4x^2 = 1/4(3)^2 = 9/4 (not correct)
C. Y = 16x^2
Plugging in the values from the table:
For x = 0, 16x^2 = 16(0)^2 = 0 (correct)
For x = 1, 16x^2 = 16(1)^2 = 16 (correct)
For x = 2, 16x^2 = 16(2)^2 = 64 (not correct)
For x = 3, 16x^2 = 16(3)^2 = 144 (not correct)
D. Y = 1/16x^2
Plugging in the values from the table:
For x = 0, 1/16x^2 = 1/16(0)^2 = 0 (not correct)
For x = 1, 1/16x^2 = 1/16(1)^2 = 1/16 (not correct)
For x = 2, 1/16x^2 = 1/16(2)^2 = 1/16 (not correct)
For x = 3, 1/16x^2 = 1/16(3)^2 = 9/16 (not correct)
Therefore, the equation that is true for all the ordered pairs in the table is option C. Y = 16x^2.
To determine which equation is true for all the ordered pairs in the table, we need to analyze the pattern in the Y-values corresponding to the given X-values.
By observing the table, we can see that the Y-values increase as the X-values increase. Furthermore, the relationship between the X-values and the Y-values suggests that the Y-values are derived from squaring the X-values and then possibly multiplying by a constant.
Let's calculate the Y-values for each X-value in the table using the equation options provided:
1. For option A: Y = 4x^2
For X = 0, Y = 4(0)^2 = 0
For X = 1, Y = 4(1)^2 = 4
For X = 2, Y = 4(2)^2 = 16
For X = 3, Y = 4(3)^2 = 36
2. For option B: Y = (1/4)x^2
For X = 0, Y = (1/4)(0)^2 = 0
For X = 1, Y = (1/4)(1)^2 = 1/4
For X = 2, Y = (1/4)(2)^2 = 1
For X = 3, Y = (1/4)(3)^2 = 9/4
3. For option C: Y = 16x^2
For X = 0, Y = 16(0)^2 = 0
For X = 1, Y = 16(1)^2 = 16
For X = 2, Y = 16(2)^2 = 64
For X = 3, Y = 16(3)^2 = 144
4. For option D: Y = (1/16)x^2
For X = 0, Y = (1/16)(0)^2 = 0
For X = 1, Y = (1/16)(1)^2 = 1/16
For X = 2, Y = (1/16)(2)^2 = 1/4
For X = 3, Y = (1/16)(3)^2 = 9/16
After calculating the Y-values for each equation option, we can see that option A: Y = 4x^2 matches all the Y-values from the given table (0, 4, 16, 36).
Therefore, the correct equation for all the ordered pairs in the table is A. Y = 4x^2.