Question

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

Explanation:

Step1: Analyze sign of coefficients

For $y=k|x|$:

• If the graph opens upward, $k>0$; if downward, $k<0$.
• $y=A|x|$ opens upward: $A>0$
• $y=B|x|$ opens upward: $B>0$
• $y=C|x|$ opens downward: $C<0$
• $y=D|x|$ opens downward: $D<0$

Step2: Identify coefficient closest to 0

The smaller the absolute value of $k$, the wider the graph. $y=B|x|$ is the widest, so $|B|$ is smallest, meaning $B$ is closest to 0.

Step3: Find coefficient with least value

Negative coefficients are smaller than positive ones. Narrower downward-opening graphs have more negative (smaller) $k$. $y=C|x|$ is wider than $y=D|x|$, so $C > D$, making $D$ the least value.

Answer:

(a)
A: Positive
B: Positive
C: Negative
D: Negative

(b)
$\boldsymbol{B}$

(c)
$\boldsymbol{D}$