<s>[INST] Solve $f(x) = ax^2 + bx + c$ to find the value of $K$ $f(x)=ax^2+bx+c$, where $a=-9$, $b=12$ and $c=16$. If $$-1<f'(x)<1$$ then $h<x<k$. To $2$ decimal places, what is the value of $k$? 

Hi, this is working for solving $f(x) = ax^2 + bx + c$ to find the value of $K$
I used Quadratic Equation to solve for x and got the answer for 
$x = -0.824045318$ or $2.157378652$
Hence, the value of K is -0.82
Did I used the correct formula to solve this question?
 [/INST] well, suppose $f(x) = ax^2 + bx + c $, then $f'(x) = 2ax + b $. If $-1 < f'(x) < 1$, then
$$ -1 < 2ax + b < 1 \iff -b-1 < 2ax < 1 - b \iff - \frac{b+1}{2a} < x < \frac{1-b}{2a}$$
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