Question

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Answer 1

Answer:

Step-by-step explanation:

Given is a function

$f(x) = x^2 + 5x + 6$

Since leading term is positive,

the parabola is open up.

Let us write this in vertex form after completing the square

$f(x) = x^2 +2(\frac{5}{2})x+\frac{25}{4} -\frac{25}{4}+6\\=(x+(\frac{5}{2})^2-\frac{1}{4}$

Hence we get vertex= (-5/2,-1/4)

Since this is a parabola open up we have the minimum point is only one at x=-5/2

So we have the function decreasing for x<-2.5 and increasing for x>-2.5

Decreases in $(-\infty, -2.5)$

Increases in $(-2.5,\infty)$