The left parabola is a reflection of the right parabola. Enter the corodinate on the left parabola that corresponds to the identified coordinate on the right parabola.

Question

Left parabola: y = (-x - 2)^2
Right parabola: f (x) = (x - 2)^2
Right parabola point: (3, 1)

Answer 1

To find the corresponding point on the left parabola \( y = (-x - 2)^2 \) that reflects the point \((3, 1)\) on the right parabola \( f(x) = (x - 2)^2 \), we first need to understand the reflection across the y-axis.

1. Identify the corresponding x-coordinate on the left parabola: The reflection of the x-coordinate of the point (3, 1) across the y-axis is \(-3\).

2. Use the left parabola equation to find the corresponding y-coordinate: We substitute \( x = -3 \) into the left parabola's equation: \[ y = (-(-3) - 2)^2 = (3 - 2)^2 = (1)^2 = 1. \]

So, the corresponding coordinate on the left parabola is \((-3, 1)\).

Therefore, the answer is \(\boxed{(-3, 1)}\).