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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

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

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

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

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

To determine which ordered pair is part of the solution set for the equation \( y = 5x^2 - 2 \), we need to substitute the x-values from each ordered pair into the equation and see if the resulting y-value matches the y-value from the pair.

  1. For \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The pair \( (-1, 3) \) is a solution.

  2. For \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The pair \( (-1, 43) \) is NOT a solution.

  3. For \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The pair \( (1, 5) \) is NOT a solution.

  4. For \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The pair \( (-1, 5) \) is NOT a solution.

So the only ordered pair from the given options that is part of the solution set for the equation \( y = 5x^2 - 2 \) is:

(−1, 3)