15. Let $a>0, x \in[-1,1]$. When the function $y=-x^{2}-a x+b$ has a minimum value of -1 and a maximum value of 1, find the corresponding values of $x$ for which the function attains its minimum and maximum values.
15. $y=f(x)=-\left(x+\frac{a}{2}\right)^{2}+b+\frac{a^{2}}{4}$. Since $a>0$, the axis of symmetry is the line $x=-\frac{a}{2}2$, so $y_{\text {max }}=f(-1)=-1+$ $a+b=1$, which means $a+b=2$, thus $a=b=1$, contradicting $a>2$; if $-\frac{a}{2} \geqslant-1$, i.e., $0<a \leqslant 2$, then $y_{\max }=$ $f\left(-\frac{a}{2}\right)=b+\frac{a^{2}}{4}=1$, thus $a=b=-2+2 \sqrt{2}$.