Question

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)

Answer 1

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

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

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

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

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

From this analysis, the ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is \((-1, 3)\).