Answer:
- increasing: (-∞, 0)
- decreasing: (0, ∞)
Step-by-step explanation:
The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...
increasing from -∞ to 0 (not including 0)
decreasing from 0 to +∞ (not including 0)
_____
At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.
Answer:
First image attached
The error was done in Step E, because student did not multiply
by the negative sign in numerator. Step E must be
.
Second image attached
The error was done in Step C, because the student omitted the
of the algebraic identity
. Step C must be 
Step-by-step explanation:
First image attached
The error was done in Step E, because student did not multiply
by the negative sign in numerator. The real numerator in Step E should be:

Hence, Step E must be
.
Second image attached
The error was done in Step C, because the student omitted the
of the algebraic identity
. Step C must be 
And further steps are described below:
Step D

Which according to the Quadratic Formula, represents a polynomial with complex roots. That is: (
,
,
)


(Conjugated complex roots)
Step E

Step F

Answer:
the answer is ac line segment