look at the graphs and their equations below. then fill in the information about the coefficients a, b, c…

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: (choose one) b: (choose one) c: (choose one) d: (choose one) (b) choose the coefficient with the greatest value. a b c d (c) choose the coefficient closest to 0. a b c d

Answer

Explanation:

Step1: Analyze the graph of (y = A|x|)

The graph of (y = A|x|) is a 'V - shaped' graph. If (A>0), the 'V' opens upwards, and if (A < 0), the 'V' opens downwards. The larger the absolute - value of (A), the steeper the graph.

Step2: Determine the sign of the coefficient

For the graph of (y = A|x|), if the 'V' opens upwards, (A>0), and if it opens downwards, (A < 0). For (y = B|x|), if it opens upwards, (B>0), for (y = C|x|), if it opens downwards, (C < 0), and for (y = D|x|), if it opens downwards, (D < 0).

Step3: Compare the magnitudes of the coefficients

The steepness of the graph of (y = k|x|) is determined by (|k|). A steeper graph has a larger (|k|).

Let's assume the standard - form of the absolute - value function (y = k|x|). When (x = 1), (y=|k|).

For the graph of (y = A|x|), it is less steep than (y = B|x|) and opens upwards, so (A>0) and (|A|<|B|). The graph of (y = B|x|) opens upwards and is steeper than (y = A|x|), so (B>0) and (|B|>|A|). The graph of (y = C|x|) opens downwards, so (C < 0). The graph of (y = D|x|) opens downwards and is steeper than (y = C|x|), so (D < 0) and (|D|>|C|).

(a) For (y = A|x|): Positive For (y = B|x|): Positive For (y = C|x|): Negative For (y = D|x|): Negative

(b) Since the graph of (y = B|x|) is the steepest among the upward - opening graphs, (B) has the greatest value.

Answer:

(a) (A): Positive, (B): Positive, (C): Negative, (D): Negative (b) (B) (c) (A)