How can dilation parameter a in wavelet leads to sign reversal?

Question

I am studying wavelets and it has been given that $$\psi_{a,b} = \frac{1}{\sqrt{|a|}} \psi (\frac{t-b}{a})$$ now the function $$ \psi(t)= \begin{cases} 1,& \text{if } 0\leq t<\frac 12\\ -1, & \text{if } \frac 12\leq t<1\\ 0& \text{otherwise} \end{cases} $$ is given as in terms of previous equation $$\psi_{a,b}= \frac {1} {\sqrt{a}}[u(t-a)-2u(t-b-\frac a2)+u(t-b-a)]$$ when a>0 and $$\psi_{a,b}=- \frac {1} {\sqrt{-a}}[u(t-a)-2u(t-b-\frac a2)+u(t-b-a)]$$ when a<0. My issue is, how can 'a' which is a dilation parameter can lead to something like a negative function when a<0?