SOLUTION: The amount of carbon dioxide (in pounds per 15,000 miles) released by a typical SUV depends on its fuel efficiency according to the formula below, where x is the fuel efficiency of

Algebra ->  Functions -> SOLUTION: The amount of carbon dioxide (in pounds per 15,000 miles) released by a typical SUV depends on its fuel efficiency according to the formula below, where x is the fuel efficiency of      Log On


   

Question 215089: The amount of carbon dioxide (in pounds per 15,000 miles) released by a typical SUV depends on its fuel efficiency according to the formula below, where x is the fuel efficiency of an SUV in miles per gallon.
W = 32x2 − 1952x + 42,000 (12 ≤ x ≤ 33)

According to the model, what is the fuel efficiency of the SUV with the least carbon dioxide pollution?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the fuel efficiency with the least carbon dioxide pollution, simply find the vertex of y=32x%5E2-1952x%2B42000



In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=32x%5E2-1952x%2B42000, we can see that a=32, b=-1952, and c=42000.


x=%28-%28-1952%29%29%2F%282%2832%29%29 Plug in a=32 and b=-1952.


x=%281952%29%2F%282%2832%29%29 Negate -1952 to get 1952.


x=%281952%29%2F%2864%29 Multiply 2 and 32 to get 64.


x=61%2F2 Reduce.


So the x-coordinate of the vertex is x=61%2F2. Note: this means that the axis of symmetry is also x=61%2F2.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


y=32x%5E2-1952x%2B42000 Start with the given equation.


y=32%2861%2F2%29%5E2-1952%2861%2F2%29%2B42000 Plug in x=61%2F2.


y=32%283721%2F4%29-1952%2861%2F2%29%2B42000 Square 61%2F2 to get 3721%2F4.


y=29768-1952%2861%2F2%29%2B42000 Multiply 32 and 3721%2F4 to get 29768.


y=29768-59536%2B42000 Multiply -1952 and 61%2F2 to get -59536.


y=12232 Combine like terms.


So the y-coordinate of the vertex is y=12232.


So the vertex is which in decimal form is (30.5, 12232)


Since the y-coordinate is the max/min value, this means that the lowest carbon emission is 12,332 pounds per 15000 miles.