Question

The functions below represent the amounts of water released from two reservoirs over x weeks:

Reservoir A

f(x) = x2 – 7x + 5

Reservoir B

g(x) = 3x2 – 6x + 2

The function h(x) = f(x) – g(x) represents the difference in the amounts of water released.

Determine which statements about h(x) and about the reservoirs are true. Check all that apply.

h(x) = –2x2 – 13x + 6
h(x) = –2x2 – x + 3
Reservoir A releases less water than Reservoir B over 1 week.
Reservoir A releases the same amount of water as Reservoir B over 1 week.
Reservoir A releases more water than Reservoir B over 1 week.

Answer 1

Answer:

• h(x) = -2x^2 -x +3
• Reservoir A releases the same amount of water as Reservoir B over 1 week

Step-by-step explanation:

Given:

  f(x) = x^2 -7x +5

  g(x) = 3x^2 -6x +2

  h(x) = f(x) -g(x)

Find:

  h(x)

  h(1)

Solution:

The expression for h(x) is found by evaluating its definition:

  h(x) = (x^2 -7x +5) -(3x^2 -6x +2)

  h(x) = x^2(1 -3) +x(-7 -(-6)) +(5 -2)

  h(x) = -2x^2 -x +3

Then h(1) is found by substituting 1 for x:

  h(1) = -2(1^2) -(1) +3 = -2 -1 +3

  h(1) = 0 . . . . difference in release amounts after 1 week is 0

The true statements are ...

• h(x) = -2x^2 -x +3
• Reservoir A releases the same amount of water as Reservoir B over 1 week

Answer 2

Answer:

B and D

Step-by-step explanation:

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