Question

look at the graphs and their equations below. then fill in the information about the coefficients a, b, c, and d.
(a) for each coefficient, choose whether it is positive or negative.
a: positive
b: (choose one)
c: (choose one)
d: (choose one)
(b) choose the coefficient closest to 0.
(c) choose the coefficient with the least value.

Explanation:

Step1: Recall the property of $y = k|x|$ graph

If $k>0$, the graph of $y = k|x|$ opens upwards. If $k < 0$, the graph of $y=k|x|$ opens down - wards.

Step2: Analyze graph of $y = B|x|$

The graph of $y = B|x|$ opens upwards, so $B>0$.

Step3: Analyze graph of $y = C|x|$

The graph of $y = C|x|$ opens upwards, so $C>0$.

Step4: Analyze graph of $y = D|x|$

The graph of $y = D|x|$ opens down - wards, so $D<0$.

Step5: Compare positive coefficients

For positive coefficients, the larger the coefficient, the steeper the graph. Among $A$, $B$, and $C$, the graph of $y = C|x|$ is the steepest and $y = B|x|$ is the least steep.

Step6: Determine the least - value coefficient

Since $D$ is negative and $A$, $B$, $C$ are positive, the coefficient with the least value is $D$.

Answer:

(a) B: positive; C: positive; D: negative
(b) B
(c) D