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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

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

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

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

(−1,3)

1 answer

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

  1. For \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( 43 \).

  2. For \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( 5 \).

  3. For \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( 5 \).

  4. For \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This matches \( 3 \).

The only ordered pair that is part of the solution set for the equation is \( (-1, 3) \).