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

Question

?

(1 point)
Responses

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

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

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

(−1,5)

Answer 1

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

1. For the pair \((-1, 43)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] (not equal to 43)

2. For the pair \((-1, 3)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] (equal to 3, so this pair is a solution)

3. For the pair \((1, 5)\): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] (not equal to 5)

4. For the pair \((-1, 5)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] (not equal to 5)

The only ordered pair that satisfies the equation is \((-1, 3)\).

So, the correct answer is: \((-1, 3)\)