My wife went back to school and is taking Algebra. I haven't been to school in years and am trying to help her, I'm not looking for the answers, but to be reminded of the steps to do the math so that I can in turn show her how.

The original problem is at the bottom.

If I remember correctly, P(x) means the profit of x and it is not a multiplication equation.

Formula:

P (x) = - 3.2 x² + 268.2 x + 257 or read it as the Profit of x = - 3.2 x² + 268.2 x + 257

x = items produced per day

If that is correct, I have the following

**2.)**

x = 40

P(40) = -3.2(40²) + 268.2(40) + 257

P(40) = -5120 + 10728 + 257

Profit of (40 items) = 5865

**3.)**

x = 50

P(50) = -3.2(50²) + 268.2(50) + 257

P(50) = -8000 + 13410 + 257

Profit of (50 items) = 5667

**4.)**

Should this be as follows? 5423 = -3.2(x²) + 268.2(x) + 257 . I tried this way, and then I tried to convert the numbers to standard equation, making them all whole numbers, but I can't figure out a way to do that for both values that have a decimal place.

**5.)**

I'm not sure how to calculate this, besides going through it via attrition

A manufacturing company found that the equation P(x) = - 3.2x2 +268.2x + 257 could be used to approximate their profit per day for x items produced.

For each of the following, show all calculation methods and explain your results in complete sentences.

1. This is an equation for “profit”. What, besides selling price, determines the “profit” from the sale of an item? Explain using at least 3 specific ideas.

2. Find the profit if 40 items are made.

3. Find the profit if 50 items are made. How does this compare to the profit from making 40 items? Does this result seem reasonable? Explain.

4. How many objects would need to be made to get a profit of $5,423? Be sure to show the solution process step-by-step.

5. How many objects should be sold to maximize the profit? What is the maximum profit?

6. Show a graph of the profit equation. Be sure to label the horizontal and vertical axes.

• Label the y-intercept with an ordered pair of numbers. Explain these values in the context of the problem.

• Label both x-intercepts with ordered pairs of numbers, approximating values to the nearest tenth. Explain these values in the context of the problem.

• Label the vertex with an ordered pair of numbers. Explain these values in the context of the problem.

7. Explain why a profit equation could be useful to a manufacturing company in planning their business.