Solving Linear-Quadratic Systems by Substitution

Erin and Kristen are playing a game, tossing balls back and forth. They are trying to toss balls to each other at the same time, in opposite directions, but the balls keep bumping into each other!

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If Erin throws her ball in the parabola given by $y=-2x^2+x+3$, which of the following paths for Kristen's ball will not cause a collision?