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.
(b) choose the coefficient closest to 0.
(c) choose the coefficient with the least value.

Explanation:

Step1: Analyze the sign of the coefficient

The graph of $y = k|x|$ opens upwards if $k>0$ and down - wards if $k < 0$. For $y = A|x|$, the graph opens upwards, so $A>0$. For $y = B|x|$, the graph opens upwards, so $B>0$. For $y = C|x|$, the graph opens upwards, so $C>0$. For $y = D|x|$, the graph opens downwards, so $D<0$.

Step2: Analyze the magnitude and proximity to 0

The larger the absolute - value of the coefficient of $|x|$, the steeper the graph. Among positive coefficients, a smaller positive value is closer to 0. Comparing the positive - valued graphs of $y = A|x|$, $y = B|x|$, and $y = C|x|$, the graph of $y = B|x|$ is the least steep among them, so $B$ is the positive coefficient closest to 0.

Step3: Compare the values

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

Answer:

(a) A: positive, B: positive, C: positive, D: negative
(b) B
(c) D