Question
A potter is selling vases. The function gives the total profit p(x) , in dollars, the potter will receive if the vases are sold at a price of x dollars each. The graph of y = p(x) is shown.
What equation represents the relationship between the price of one vase and the profit?
The correct answer is:
HINT : find the equation of p(x) using a general quadratic equation with 2 roots.
Explanation :
Step 1:
Let p(x) be a quadratic equation with two roots and is inverted then the general equation is
p(x) = -a(x-2)(x-34) ( where x = 2,34 are roots of the equation )
We can rewrite (x-2)(x-34) as (x-18 +16)(x-18 -16)
It is in the form of (a - b)(a + b) so we can write it as 
.
Here a= (x-18) and b = 16
The -a(x-2)(x-34) as -a (x-18 +16)(x-18 -16) = 
Step 2:
But from the graph we know that the point (18,1536) lies on the graph so substitute them to get the equation of p(x).
The the final equation p(x) = 
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Those who responded to the pool were not a random sample of the population of the United States. Moreover, because the people were watching a US cable news show, it could not have been very objective. Thus the majority of those watching it shared the same political bias. Therefore, the program's viewers might need to accurately represent the entire American populace.
Getting highly responsive is not something that has any percentage of yes or no responses because what we're trying to find out is how people feel about it. So having 50-50 people is not a condition that the show needed to allow more time to respond to the information. So we need to know the time taken to respond to the pool and what percentage of people were at a discount.
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