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 with the least value.
○ a ○ b ○ c ○ d
(c) choose the coefficient closest to 0.
○ 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 → $A$ positive
• $y=B|x|$: opens upward → $B$ positive
• $y=C|x|$: opens downward → $C$ negative
• $y=D|x|$: opens downward → $D$ negative

Step2: Compare coefficient magnitudes

The steeper the graph, the larger $|k|$:

• $B$ is steeper than $A$ → $|B|>|A|>0$
• $C$ is steeper than $D$ → $|C|>|D|>0$, so $C
• Order of values: $C

Step3: Answer part (b)

Least value is the smallest number, which is $C$.

Step4: Answer part (c)

Closest to 0 is the number with smallest absolute value, which is $A$.

Answer:

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

(b) $\boldsymbol{C}$

(c) $\boldsymbol{A}$