15 26. (1) When it intersects both the positive and negative halves of the $x$-axis, there are $P_{3}^{1} \cdot P_{3}^{1} \cdot P_{2}^{1}=18$ lines; (2) When it passes through the origin and intersects the negative half of the $x$-axis, $c=0$ and $a b>0$, there are $P_{3}^{2}=6$ lines; (3) When it intersects the negative half of the $x$-axis at two points, $\Delta \geqslant 0$ and $\frac{b}{a}>0, \frac{c}{a}>0$ imply $\Delta \geqslant 0$ and $a, b, c$ have the same sign, thus $b=3, a, c$ are chosen from $1, 2$, yielding $P_{2}^{2}$ lines. Therefore, there are a total of 26 lines.
15 From the five numbers $-1, 0, 1, 2, 3$, select three (without repetition) to form the coefficients of the quadratic function $y=a x^{2}+b x+c$. The number of different parabolas that intersect the negative direction of the $x$-axis at least once is