[latex] Left align block of equations

I want to left align a block of equations. The equations in the block itself are aligned, but that's not related at all to my question! I want to left align the equations rather than have them centered all the time, because it looks dumb with narrow centered equations.

Example, I want to left align this

\begin{align*}
    |\vec a| &= \sqrt{3^{2}+1^{2}} = \sqrt{10} \\
    |\vec b| &= \sqrt{1^{2}+23^{2}} = \sqrt{530} \\ 
    \cos v &= \frac{26}{\sqrt{10} \cdot \sqrt{530}} \\
    v &= \cos^{-1} \left(\frac{26}{\sqrt{10} \cdot \sqrt{530}}\right) \\
    v &= \uuline{69.08...\degree}
\end{align*}    

but also this

\begin{align*}
    f(x) = -1.25x^{2} + 1.5x
\end{align*}

How is this done? If it's even possible.

The fleqn option in the document class will apply left aligning setting in all equations of the document. You can instead use \begin{flalign}. This will align only the desired equations.

Try this:

\begin{flalign*}
    &|\vec a| = \sqrt{3^{2}+1^{2}} = \sqrt{10} & \\
    &|\vec b| = \sqrt{1^{2}+23^{2}} = \sqrt{530} &\\ 
    &\cos v = \frac{26}{\sqrt{10} \cdot \sqrt{530}} &\\
    &v = \cos^{-1} \left(\frac{26}{\sqrt{10} \cdot \sqrt{530}}\right) &\\
\end{flalign*}

The & sign separates two columns, so an & at the beginning of a line means that the line starts with a blank column.

You can use \begin{flalign}, like the example bellow:

\begin{flalign}
    &f(x) = -1.25x^{2} + 1.5x&
\end{flalign}