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.

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 ...

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

47 - 90 = 43

43 - 180 = x

x = 137