### Home > CALC > Chapter 4 > Lesson 4.4.3 > Problem4-152

4-152.

Find the value for $a$ below so that $f(x)$ is continuous at $x = 3$.

$f ( x ) = \left\{ \begin{array} { c c } { | 4 - 3 x | } & { \text { for } x < 3 } \\ { a x ^ { 2 } + 2 } & { \text { for } x \geq 3 } \end{array} \right.$

We need to find a value of $a$ such that:

Substitute the left piece of $f(x)$ and the right piece of $f(x)$.

Evaluate the limits: $5 = 9a + 2$

Solve for $a$: