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

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) (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

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: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Negate to get .

Multiply 2 and to get .

Reduce.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

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

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

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.

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