Question

y=5x^2-2
which ordered pair is it? (-1,3) (-1,43) (-1,5) (1,5)

Answer 1

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

1. For the pair \((-1, 3)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The ordered pair \((-1, 3)\) is a solution.

2. For the pair \((-1, 43)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The ordered pair \((-1, 43)\) is **not** a solution.

3. For the pair \((-1, 5)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The ordered pair \((-1, 5)\) is **not** a solution.

4. For the pair \((1, 5)\):
\[
y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3
\]
The ordered pair \((1, 5)\) is **not** a solution.

The only ordered pair that satisfies the equation \( y = 5x^2 - 2 \) is \((-1, 3)\).