Question 1

Given the quadratic function $$f(x) = ax^2$ + bx + c$$, which of the following statements is TRUE about its graph?

Accepted Answer

The axis of symmetry is $$x = -\frac{b}{2a}.$$

Question 2

Suppose the revenue function for a product is $$R(x) = 50x - x^2$. What is the break-even quantity if the cost function is C(x) = 10x + 100$?

Accepted Answer

$$x = 5 or$$ $$x = 20$$

Question 3

A company’s profit function is $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and at how many units is it achieved?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$ units.

Question 4

Which of the following is the correct formula for the vertex of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$\left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right)$$

Question 5

If the leading coefficient $$a of a $$polynomial function $$f(x) is $$negative, what happens to the graph as $$x$$ becomes a large positive number?

Accepted Answer

The graph falls to negative infinity.

Question 6

A seminar charges $$600$$ per person and attracts $$1000$$ people. For each $$20$$ decrease in price, $$100$$ more people attend. What price per person maximizes revenue?

Accepted Answer

$$400$$

Question 7

Which of the following is NOT a property of polynomial functions?

Accepted Answer

A polynomial of odd degree has both ends going in the same direction.

Question 8

Given $$f(x) = 4x^2$ + 3x - 9$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$-\frac{3}{8}$$

Question 9

If $$f(x) = 2x^3$ - 5x^2$ + 3x - 7$$, what is the degree and leading coefficient of the polynomial?

Accepted Answer

Degree $$3$$, leading coefficient $$2$$

Question 10

A business’s cost function is $$C(x) = 100 + 20x$$ and revenue function is $$R(x) = 50x. $$What is the break-even quantity?

Accepted Answer

$$x = 4$$

Question 11

Which of the following best describes the y-intercept of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

It is at $$(0, c).$$

Question 12

If a polynomial function $$f(x)$$ has degree $$n$$, what is the maximum number of turning points it can have?

Accepted Answer

$$n-1$$

Question 13

Suppose $$f(x) = -x^2$ + 6x + 5. $$What is the maximum value of $$f(x)$$?

Accepted Answer

$$23$$

Question 14

Which of the following is a correct definition of a polynomial function of degree $$n$$?

Accepted Answer

$$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$, where a_n$$ 
eq 0$$

Question 15

A company’s revenue function is $$R(x) = 100x - 2x^2$. What is the maximum revenue?

Accepted Answer

$$2500 at$$ $$x = 25$$

Business Calculus Study Notes: Nonlinear Functions and Quadratic Applications

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