Question

A quadratic function f(x)f is hidden from view. You must find all intervals where f(x) is positive. Choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently.

Answer 1

To find the positive intervals, we'll have:

`-3x^2-18x-15>0`

1. Divide both sides by -3:

(Remember that dividing or multiplying by a negative number turns the inequality around!)

`\begin{gathered} -3x^2-18x-15>0 \\ \rightarrow x^2+6x+5<0 \end{gathered}`

2. Factor the expression:

`\begin{gathered} x^2+6x+3<0 \\ \rightarrow(x+5)(x+1)<0 \end{gathered}`

3. Identify the interval we're looking for:

Therefore, the function is positive in the interval:

[tex]\begin{gathered} -5