Which of the following tables of values is correct for the equation y = -3x^2?
There is only one correct table of values for the equation y = -3x^2, which is:
| x | y |
| -2 | -12 |
| -1 | -3 |
| 0 | 0 |
| 1 | -3 |
| 2 | -12 |
To find the value of y for a given value of x, simply substitute x into the equation and evaluate. For example, when x = -2:
y = -3(-2)^2 = -3(4) = -12
and when x = 2:
y = -3(2)^2 = -3(4) = -12
Note that the graph of this equation is a downward-facing parabola, symmetrical around the y-axis, with the vertex at (0,0).
To determine the correct table of values for the equation y = -3x^2, we can substitute various x-values into the equation and calculate the corresponding y-values. Let's calculate the values using three different x-values: -2, 0, and 2.
When x = -2:
y = -3(-2)^2
y = -3(4)
y = -12
When x = 0:
y = -3(0)^2
y = -3(0)
y = 0
When x = 2:
y = -3(2)^2
y = -3(4)
y = -12
Based on these calculations, the correct table of values for the equation y = -3x^2 is:
x | y
---------
-2|-12
0 | 0
2 |-12
To determine the correct table of values for the equation y = -3x^2, we can substitute different values of x into the equation to find the corresponding values of y.
Let's start with the equation: y = -3x^2
We can choose some values for x and calculate the corresponding values of y. By doing this for multiple x-values, we can create a table of values and determine which one is correct.
Let's consider a few arbitrary values for x and calculate the corresponding y-values.
For x = -3:
y = -3(-3)^2 = -3(9) = -27
So, when x = -3, y = -27.
For x = -2:
y = -3(-2)^2 = -3(4) = -12
So, when x = -2, y = -12.
For x = -1:
y = -3(-1)^2 = -3(1) = -3
So, when x = -1, y = -3.
For x = 0:
y = -3(0)^2 = -3(0) = 0
So, when x = 0, y = 0.
For x = 1:
y = -3(1)^2 = -3(1) = -3
So, when x = 1, y = -3.
For x = 2:
y = -3(2)^2 = -3(4) = -12
So, when x = 2, y = -12.
For x = 3:
y = -3(3)^2 = -3(9) = -27
So, when x = 3, y = -27.
Now we have the x-values matched with the corresponding y-values:
x | y
---------------
-3 | -27
-2 | -12
-1 | -3
0 | 0
1 | -3
2 | -12
3 | -27
By comparing these values with the given tables, we can determine which one is correct.