Question

“will give brainliest”

The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, sold by the company:

Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 8, 0. The vertex is at 4, 270.

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

Answer 1

Answer:

Part A: The x-intercepts represent the prices of the erasers at which the profit will be $0. The function is increasing from [-∞, 4] and decreasing from [4,+∞]. This means that when the price of the eraser is less than 4, the profit will increase until it gets to 4 and decrease for any value greater than 4, where $4 is the price at which the company has the maximum profit.

Part B: From the interval [1,4], the average rate of change is 50.625, which means that for every $1 increase in the price of erasers, the profit goes up by $50.625.

Part C:

The domain of this function is [0,+∞] because this is the only part of the function that is positive. The function cannot have -x-values because it does not make sense to make the price of an eraser 'negative'.

Step-by-step explanation:

The equation of this parabola is $f(x) = -16.875(x-4)^2 + 270$.

Part A:

The x-intercepts represent the prices of the erasers at which the profit will be $0. The function is increasing from [-∞, 4] and decreasing from [4,+∞]. This means that when the price of the eraser is less than 4, the profit will increase until it gets to 4 and decrease for any value greater than 4, where $4 is the price at which the company has the maximum profit.

Part B:

To find the average rate, we can use the slope formula, but first, we must find the y-values at each given x-value. We can plug in 1 and 4. $f(1) = -16.875(1-4)^2 + 270 = 118.125$. We know that at x = 4, the y-value is 270 because the vertex is at (4,270). Now we can apply the slope formula $\frac{270 - 118.125}{4 - 1} = 50.625$. This means that from the interval [1,4], the average rate of change is 50.625, which represents that for every $1 increase in the price of erasers, the profit goes up by $50.625.

Part C:

The domain of this function is [0,+∞] because this is the only part of the function that is positive. The function cannot have -x-values because it does not make sense to make the price of an eraser 'negative'.

hope this helped! :)