Question 1

Which of the following best describes the graph of the quadratic function $$f(x) = -2(x-3)^2$ + 5$$?

Accepted Answer

It is a parabola opening downward with vertex at $$(3, 5).$$

Question 2

Given the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the formula for the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 3

A business models its revenue with $$R(p) = -12p^2$ + 150p$$, where $$p is $$the price per unit. What price maximizes the revenue?

Accepted Answer

$$p = 6.25$$

Question 4

Which of the following statements about polynomial functions is TRUE?

Accepted Answer

The graph of a polynomial function is always continuous and has no breaks.

Question 5

What is the end behavior of the polynomial $$f(x) = -3x^4$ + x^2$ - 2$$?

Accepted Answer

Falls left, falls right

Question 6

Given $$f(x) = (x-2)^2$(x+5)^3$$, what is the multiplicity of the zero at $$x = -5$ and how does the graph behave at this zero?

Accepted Answer

Multiplicity 3; graph crosses the $$x-$$axis at $$x = -5$$

Question 7

If a polynomial $$f(x) is $$divided by $$(x - 3)$$ and the remainder is $$5$$, what is the value of $$f(3)$$?

Accepted Answer

$$5$$

Question 8

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 9

A cubic polynomial $$f(x)$$ has zeros at $$x = 1 ($$multiplicity 2) and $$x = -3 ($$multiplicity 1). Which of the following could be its factored form?

Accepted Answer

$$f(x) = (x-1)^2$(x+3)$$

Question 10

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(2, -4). $$Which of the following could be its equation?

Accepted Answer

$$f(x) = a(x-2)^2$ - 4$$

Question 11

If $$f(x) = x^4$ - 2x^2$ + 1$$, what is the degree of the polynomial and what is its leading coefficient?

Accepted Answer

Degree 4, leading coefficient 1

Question 12

A company wants to minimize the product of two numbers whose sum is 10. Let the numbers be $$x$$ and $$10-x. $$What value of $$x$$ minimizes the product?

Accepted Answer

$$x = 0 or$$ $$x = 10$$

Question 13

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

Accepted Answer

They always have at least one real zero.

Question 14

Given $$f(x) = x^3$ - 4x^2$ + x - 6$$, use the Remainder Theorem to find the remainder when $$f(x) is $$divided by $$x-2.$$

Accepted Answer

$$f(2) = 8 - 16 + 2 - 6 = -12$$

Question 15

If a polynomial $$f(x)$$ has a zero at $$x = 2 of $$multiplicity 3, what does the graph do at $$x = 2$$?

Accepted Answer

It crosses the $$x-$$axis and flattens out at $$x = 2$$

Question 16

Which of the following best describes the end behavior of $$f(x) = 2x^5$ - 7x^3$ + x$$?

Accepted Answer

Falls left, rises right

Question 17

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h = 21.9$$ meters

Question 18

Which of the following is a correct statement about the multiplicity of zeros of a polynomial?

Accepted Answer

If the multiplicity is even, the graph touches but does not cross the $$x-$$axis at the zero.

Precalculus Chapter 3 Study Notes: Quadratic and Polynomial Functions

Study Guide - Practice Questions

Study Guide - Flashcards