1. The problem asks: Which parabola has its branches closest to the Oy-axis among the following options? 2. All given parabolas have the form $y=ax^2$. The distance of the parabola's branches from the Oy-axis depends on how wide or narrow the parabola is, which is influenced by the absolute value of $a$. 3. The smaller the absolute value of $a$, the wider the parabola; the larger the absolute value of $a$, the narrower and closer the branches are to the Oy-axis. 4. Review the options: a) $y = 3x^2$ (narrow upward) b) $y = -4x^2$ (narrow downward) c) $y = \frac{1}{3}x^2$ (wider upward) d) $y = -\frac{5}{2}x^2$ (narrow downward) e) $y = \frac{4}{3}x^2$ (narrow upward) 5. Comparing the absolute values: |3|=3, |4|=4, |1/3|≈0.333, |5/2|=2.5, |4/3|≈1.333 6. The parabola with the smallest absolute $a$ (which is $\frac{1}{3}$) is the widest, meaning its branches are farthest from Oy-axis. 7. The parabola with largest absolute $a$ has narrow branches closest to Oy-axis. Between the options, $|4|=4$ is the largest, so $y = -4x^2$ is closest to Oy-axis. Final answer: The parabola $y = -4x^2$ (option b) has branches closest to the Oy-axis.