Question

look at the graphs and their equations below. then fill in the information about the leading coefficients a, b, c, and d.
$y = ax^2$ $y = bx^2$ $y = cx^2$ $y = dx^2$
(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 greatest value.
○ a ○ b ○ c ○ d

Explanation:

Step1: Sign of leading coefficient

For a parabola $y=kx^2$:

• Opens downward: $k<0$ (first two graphs: $A, B$)
• Opens upward: $k>0$ (last two graphs: $C, D$)

Step2: Narrowness vs coefficient magnitude

The smaller $|k|$, the wider the parabola:

• Widest downward parabola: $B$ (so $|B| < |A|$, $B$ closer to 0 than $A$)
• Widest upward parabola: $C$ (so $|C| < |D|$, $C$ closer to 0 than $D$)
• Overall widest parabola: $B$, so $B$ is closest to 0.

Step3: Greatest coefficient value

Positive coefficients are larger than negative ones. Among positive coefficients, $D$ has larger magnitude than $C$, so $D$ is the greatest.

Answer:

(a)

A: Negative
B: Negative
C: Positive
D: Positive

(b)

$\boldsymbol{B}$

(c)

$\boldsymbol{D}$