Which of the following ordered pairs is part of the solution set for the equation y=5x^2−2?
To find which ordered pairs are part of the solution set for the equation y = 5x^2 – 2, we substitute the x-coordinate of each ordered pair into the equation and check if the resulting y-coordinate matches:
a) (-2, -18)
Substituting x = -2 into the equation:
y = 5(-2)^2 – 2
y = 5(4) – 2
y = 20 – 2
y = 18
The y-coordinate is 18, not -18. Therefore, (-2, -18) is not part of the solution set.
b) (1, 3)
Substituting x = 1 into the equation:
y = 5(1)^2 – 2
y = 5(1) – 2
y = 5 – 2
y = 3
The y-coordinate is 3, which matches the given coordinate. Therefore, (1, 3) is part of the solution set.
c) (0, -2)
Substituting x = 0 into the equation:
y = 5(0)^2 – 2
y = 5(0) – 2
y = 0 – 2
y = -2
The y-coordinate is -2, which matches the given coordinate. Therefore, (0, -2) is part of the solution set.
Therefore, the ordered pairs that are part of the solution set for the equation y = 5x^2 – 2 are (1, 3) and (0, -2).