Question

Suppose an investor builds a stock portfolio with a variety of shares in various high tech companies. The value of the stock portfolio is modeled by the function y = 2x^2 - 20x + 100, where y is the value of the portfolio in hundreds of dollars, and x is the time in months.

a) Find the x-coordinate of the vertex. Show all work leading to your answer and write the answer in simplest form.

b) Find the y-coordinate of the vertex. Show all work leading to your answer and write the answer in simplest form.

c) What does the vertex represent for this situation? Write 1 - 2 sentences to explain your answer.

Answer 1

Explanation:

We can find the vertex either by completing the square or taking advantage of the simple formula x = -b / (2a), which provides the x-coordinate of the vertex.

Here a = 2, b = -20 and c = 100. Then the x-coordinate of the vertex is at

x = -(-20) / (2*2), or x = 5.

Next, evaluate y = 2x^2 - 20x + 100 to find the y-coordinate of the vertex. It is y(5) = 2(5^2) - 20(5) + 100, or y(5) = 50 - 100 + 100, or 50. y = 50.

The vertex is at (5, 50). This states that the stock reaches its minimum value, $50 per share), after 5 months. From that time on, the stock appreciates (increases) in value.