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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

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

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

(−1,43)

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 from each ordered pair into the equation and see if we get the corresponding y-value.

Let's calculate each option:

  1. For the ordered pair \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (Not : 5) \]

  2. For the ordered pair \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (Not : 5) \]

  3. For the ordered pair \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (Matches : 3) \]

  4. For the ordered pair \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (Not : 43) \]

Only the ordered pair \( (-1, 3) \) matches the value computed from the equation. Therefore, the correct answer is:

(−1, 3)