Question
Find $a$ and $b$ if the following function is continuous at the point or on the interval indicated against them:
$
\begin{aligned}
f(x) & =a x^2+b x+1, & & \text { for }|2 x-3| \geq 2 \\
& =3 x+2, & & \text { for } \frac{1}{2}\end{aligned}
$
$
\begin{aligned}
f(x) & =a x^2+b x+1, & & \text { for }|2 x-3| \geq 2 \\
& =3 x+2, & & \text { for } \frac{1}{2}\end{aligned}
$