1. The problem asks for the y-intercept of a parabola. 2. The y-intercept of a graph is the point where the graph crosses the y-axis. This occurs when $x=0$. 3. The parabola is given to have its vertex at the origin $(0,0)$ and is symmetric about the y-axis. 4. Since the vertex is at $(0,0)$ and the parabola passes through $(\pm 5, 5)$, the equation of the parabola can be written as: $$y = ax^2$$ 5. To find $a$, use the point $(5,5)$: $$5 = a \times 5^2 = 25a \implies a = \frac{5}{25} = \frac{1}{5}$$ 6. So the equation is: $$y = \frac{1}{5}x^2$$ 7. To find the y-intercept, substitute $x=0$: $$y = \frac{1}{5} \times 0^2 = 0$$ 8. Therefore, the y-intercept is at the point $(0,0)$. This means the parabola crosses the y-axis at the origin.