Question

Complete the following:

(a) Use the vertex formula to find the vertex of the graph of f(x)=1.5-4x-12x^2.

(b) Find the intervals where f is increasing and where f is decreasing.

Answer 1

find vertex via
\[=\frac{b}{2a}=-\frac{-4}{2\times (-12)}=-\frac{1}{6}\]

Answer 2

if you want the second coordinate of the vertex, which you do, you find
\[f(\frac{1}{6})\]

Answer 3

and since this is a parabola that opens down, it will be increasing on the interval
\[(-\infty, \frac{1}{6})\] and decreasing on
\[(\frac{1}{6},\infty)\]