Question

Which point is NOT a solution to the equation y=2x2−2
, graphed below?



(1 point)
Responses

(-1, 0)
(-1, 0)

(1, 0)
(1, 0)

(0, 2)
(0, 2)

(0, -2)
(0, -2)

Answer 1

To determine which point is not a solution to the equation \( y = 2x^2 - 2 \), we can substitute the x-values from each of the given points into the equation and verify whether the resulting y-value matches the y-value of the point.

1. For the point \((-1, 0)\):
\[
y = 2(-1)^2 - 2 = 2(1) - 2 = 2 - 2 = 0
\]
\((-1, 0)\) is a solution.

2. For the point \((1, 0)\):
\[
y = 2(1)^2 - 2 = 2(1) - 2 = 2 - 2 = 0
\]
\((1, 0)\) is a solution.

3. For the point \((0, 2)\):
\[
y = 2(0)^2 - 2 = 2(0) - 2 = 0 - 2 = -2
\]
\((0, 2)\) is **not** a solution.

4. For the point \((0, -2)\):
\[
y = 2(0)^2 - 2 = 2(0) - 2 = 0 - 2 = -2
\]
\((0, -2)\) is a solution.

The point that is **not** a solution to the equation \( y = 2x^2 - 2 \) is \((0, 2)\).