These are the $x$-intercepts, so work backwards by using the Zero Product Property to write an equation in factored form.

$\left(x - \frac{1}{2}\right)\, \, \rightarrow \, \, (2x-1)$

$y = 2x^{2} + 5x – 3$

See part (a).

$y=a(x+3)(x-2)$

Now substitute in the coordinates of the point $\left(3, −12\right)$ to solve for $a$.