To determine which ordered pair is part of the solution set for the equation \( y = 3x^2 - 4 \), we can substitute each x-value from the ordered pairs into the equation and see if the corresponding y-value matches.
Option #1: \( (-1, 1) \)
Substituting \( x = -1 \): \[ y = 3(-1)^2 - 4 = 3(1) - 4 = 3 - 4 = -1 \] So the ordered pair \( (-1, 1) \) does not match since the calculated y-value is -1.
Option #2: \( (0, 3) \)
Substituting \( x = 0 \): \[ y = 3(0)^2 - 4 = 3(0) - 4 = 0 - 4 = -4 \] So the ordered pair \( (0, 3) \) does not match since the calculated y-value is -4.
Option #3: \( (3, 1) \)
Substituting \( x = 3 \): \[ y = 3(3)^2 - 4 = 3(9) - 4 = 27 - 4 = 23 \] So the ordered pair \( (3, 1) \) does not match since the calculated y-value is 23.
None of the options provided are part of the solution set for the equation \( y = 3x^2 - 4 \). Each of the calculations has shown that the y-values do not equal the second value of the ordered pairs given.
If you need to select any one option just as part of a solution, you might note that none of them fits, but \( (-1,1) \) comes closest since it provides a valid expression (though the actual y-value calculated is -1). For the exact solutions, none are valid.
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