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

Study Guide - Practice Questions

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