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A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. An upward parabola passes through all four quadrants.

Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ?

(1 point)
Responses

(1,5)
left parenthesis 1 comma 5 right parenthesis

(−1,3)
left parenthesis negative 1 comma 3 right parenthesis

(−1,5)
left parenthesis negative 1 comma 5 right parenthesis

(−1,43)
left parenthesis negative 1 comma 43 right parenthesis

1 answer

To determine which ordered pair is part of the solution set for the equation \( y = 5x^2 - 2 \), we can evaluate the function using the x-coordinates from each ordered pair and check if the resulting y-coordinate matches.

  1. For the ordered pair (1, 5):

    • Calculate \( y \) when \( x = 1 \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
    • This does not match (1, 5), so this pair is not a solution.

  2. For the ordered pair (−1, 3):

    • Calculate \( y \) when \( x = -1 \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
    • This does not match (−1, 3), so this pair is not a solution.

  3. For the ordered pair (−1, 5):

    • Using the same \( x = -1 \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
    • This does not match (−1, 5), so this pair is not a solution.

  4. For the ordered pair (−1, 43):

    • Using \( x = -1 \) again: \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
    • This does not match (−1, 43), so this pair is not a solution.

After evaluating all the options, none of the provided ordered pairs satisfy the equation \( y = 5x^2 - 2 \). Please check the options or the context of the question once again, as it seems there may be no correct answer among the provided pairs.