Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #15 : Quadratic Formula

The height of a kicked soccer ball can be modeled with the equation

H(x)=-4.9x^2 +15x +0.5 ,

where the height is given in meters and is the time in seconds. At what time(s) will the ball be 2 meters off the ground?

Possible Answers:

x=0.412 seconds

x=1.244 seconds

x=0.104 seconds

x=2.958 seconds

x=1.244 seconds

x=0.104 seconds

Correct answer:

x=0.104 seconds

x=2.958 seconds

Explanation:

Set up the equation to solve for the time when the height is at 2 meters:

2=-4.9x^2+15x-0.5

Now put the equation into quadratic form ax^2+bx+c=0 so that we can solve it using the quadratic formula

-4.9x^2+15x-1.5=0 .

The quadratic equation is

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

where a=-4.9 , b=15 , and c=-1.5 .

Solving for gives us two possible values,

x=0.104 seconds

x=2.958 seconds.

Report an Error

Example Question #11 : Quadratic Formula

Solve for .

x^2+4x+5=0

Possible Answers:

x=2, -2

x=0, -4

x=-2

$\textup{Answer is not present}$

Correct answer:

$\textup{Answer is not present}$

Explanation:

When applying the quadratic formula, the discriminant (portion under the square root) is negative and so there are no real roots of the equation shown.

Report an Error

Example Question #475 : Intermediate Single Variable Algebra

Solve for x

(x+2)^2+2x+2=0

Possible Answers:

x=-9, -3

$x=3\pm\sqrt{3}$

x=-1, -5

$x=-3\pm{\sqrt{3}}$

Correct answer:

$x=-3\pm{\sqrt{3}}$

Explanation:

Once the square is multiplied out and the equation simplified, it yields x^2+6x+6=0 , a good time for the quadratic formula, $x=\frac{-b\pm{\sqrt{b^2-4ac}}}{2a}$ where a, b, c are the coefficients of the polynominal in descending order. Plug in a=1, b=6, c=6, and it yields $-3\pm{\frac{\sqrt{12}}{2}}$ , multiply out the square root and it yields $-3\pm{\sqrt{3}}$ .

Report an Error

Example Question #476 : Intermediate Single Variable Algebra

Using the quadratic equation, find the roots of the following expression.

2x^2+5x - 12

Possible Answers:

x=-4

x=-1.5

x = -4

$x = \frac{2}{3}$

x =-4

x=1.5

x=4

x = 1.5

No real solutions

Correct answer:

x =-4

x=1.5

Explanation:

To find the roots of the quadratic expression, we must use the quadratic equation

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

Plugging in our values for , , and (, , and , respectively) we get the equation:

$x = \frac{-5\pm\sqrt{25-4(2)(-12)}}{2\cdot2}$

First, let's simplify the radical:

$x=\frac{-5\pm\sqrt{25+96}}{4}$

which becomes

$x=\frac{-5\pm\sqrt{121}}{4}$

$x=\frac{-5\pm11}{4}$

Now that we've simplified the radical, we need to solve for both solutions:

$x_1=\frac{-5+11}{4}=\frac{6}{4}=\frac{3}{2}=1.5$

and

$x_2=\frac{-5-11}{4}=\frac{-16}{4}=-4$

Therefore, the roots of this quadratic expression are x=1.5 and x=-4 .

Report an Error

Example Question #311 : Quadratic Equations And Inequalities

Find the roots of the following equation using the quadratic formula:

f(x) = 3x^2 + 8x - 3

Express in simplest form.

Possible Answers:

$x = \frac{-8\pm10}{6}$

$x = \frac{-4\pm5}{3}$

$x = \frac{-8\pm2\sqrt{7}}{6}$

$x = \frac{-4\pm\sqrt{7}}{3}$

$x = \frac{-8\pm\sqrt{28}}{6}$

Correct answer:

$x = \frac{-4\pm5}{3}$

Explanation:

Remember the quadratic equation. For any quadratic polynomial, ax^2 + bx + c , the roots of the function are given by:

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

In this situation, we have 3x^2 + 8x -3 , so a = 3, b = 8, c = -3 .

Substituting into the formula, we get the roots at:

$x = \frac{-8\pm\sqrt{8^2-4(3\cdot-3)}}{2\cdot3}$

Simplifying gives us:

$x = \frac{-8\pm\sqrt{64+36}}{6} = \frac{-8\pm\sqrt{100}}{6} = \frac{-8\pm10}{6} = \frac{-4\pm5}{3}$ .

Report an Error

Example Question #2 : How To Use The Quadratic Function

Which of the following is the correct solution when x^2-10x-11=0 is solved using the quadratic equation?

Possible Answers:

$\frac{-10\pm 12}{2}$

$10\pm 12$

$\frac{10\pm \sqrt{56}}{2}$

$\frac{10\pm 12}{2}$

Correct answer:

$\frac{10\pm 12}{2}$

Explanation:

$x=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-11)}}{2(1)}$

$=\frac{10\pm \sqrt{100+44}}{2}$

$=\frac{10\pm \sqrt{144}}{2}$

$=\frac{10\pm 12}{2}$

Report an Error

Example Question #311 : Quadratic Equations And Inequalities

Solve the equation using the quadratic formula.

$x^2+5x+\frac{9}{4}=0$

Possible Answers:

7,9

$\frac{1}{2}, \frac{9}{2}$

-5,2

$-\frac{1}{2}, -\frac{9}{2}$

Correct answer:

$-\frac{1}{2}, -\frac{9}{2}$

Explanation:

The quadratic formula is

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

Setting a=1 , b=5 , $c=\frac{9}{4}$ yields,

$\\ \frac{-5\pm\sqrt{5^2-4(1)(\frac{9}{4})}}{2(1)}\\ \\=\frac{-5\pm\sqrt{25-9}}{2} \\ \\=-\frac{5}{2}\pm2 \\ \\ = -\frac{1}{2}, -\frac{9}{2}$

Report an Error

Example Question #481 : Intermediate Single Variable Algebra

Find the roots of: y=x^2-x+100

Possible Answers:

$\pm10$

Since the quadratic cannot be factored, there are no roots.

$\frac{1\pm \sqrt{401}}{2}$

$\frac{1\pm i\sqrt{399}}{2}$

$\frac{1}{2}\pm i\sqrt{399}$

Correct answer:

$\frac{1\pm i\sqrt{399}}{2}$

Explanation:

Identify the values of , , and in the standard form of the parabola.

y=ax^2+bx+c

a= 1

b=-1

c=100

Calculate the discriminant.

b^2-4ac=1-4(1)(100)=-399

Since the discriminant is less than zero, the quadratic is irreducible and there are no real roots. However, there are complex roots. Use the quadratic formula to determine the complex roots.

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

$x= \frac{1\pm \sqrt{-399}}{2(1)}$

$x= \frac{1\pm i\sqrt{399}}{2}$

Report an Error

Example Question #482 : Intermediate Single Variable Algebra

Use the quadratic formula to find the roots of x^2+5x-14 .

Possible Answers:

x= 0

x=5 and x=-14

x=7 and x=-2

no solution

x=-7 and x=2

Correct answer:

x=-7 and x=2

Explanation:

The parent function of a quadratic is represented as ax^2+bx+c . The quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In this case a=1 , b=5 , and c=-14 . Replacing these values into the quadratic forumula will give you the solutions to the quadratic.

$x=\frac{-5\pm \sqrt{5^2-4(1)(-14)}}{2*1}$

$x=\frac{-5\pm \sqrt{25-(-56)}}{2}$

$x=\frac{-5\pm \sqrt{81}}{2}$

$x=\frac{-5\pm 9}{2}$

x=-7 and x=2

Report an Error

Example Question #483 : Intermediate Single Variable Algebra

Solve this quadratic equation by using the quadratic formula: x^2+4x+2

Possible Answers:

$x={-2\pm \sqrt{2}$

$x=\frac{4\pm \sqrt{8}}{2}$

$x=\frac{-4\pm \sqrt{8}}{8}$

$x=\frac{-4\pm \sqrt{8}}{1}$

$x=\frac{-4\pm \sqrt{8}}{4}$

Correct answer:

$x={-2\pm \sqrt{2}$

Explanation:

You must know the quadratic equation $x=\frac{-b\pm \sqrt{b^2-4ac}}{2}$ .

To plug in the right terms, recognize that polynomials in standard form are symbolized as ax^2+bx+c .

Plug in the values from your equation

$x=\frac{-4\pm \sqrt{4^2-4*1*2}}{2}$

simplify within the radical:

$x=\frac{-4\pm \sqrt{8}}{2}$

Simplify the radical:

$x=\frac{-4\pm2 \sqrt{2}}{2}$

Reduce:

$x={-2\pm \sqrt{2}$

Note that this represents two values since there is a $\pm$ in the equation. One is solved with an addition sign and the other is solved with a subtraction sign to yield two answers or roots where this equation crosses the x axis.

Report an Error

View Algebra 2 Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Algebra 2 Tutors

Anthony
Certified Tutor

CUNY New York City College of Technology, Bachelor of Science, Civil Engineering.

View Algebra 2 Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Chicago, SAT Tutors in New York City, Reading Tutors in Phoenix, Physics Tutors in Miami, Chemistry Tutors in Phoenix, English Tutors in San Francisco-Bay Area, Algebra Tutors in Houston, MCAT Tutors in Los Angeles, LSAT Tutors in San Diego, LSAT Tutors in Miami

Popular Courses & Classes

SSAT Courses & Classes in Seattle, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Washington DC, SAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Denver, ISEE Courses & Classes in Phoenix, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Atlanta, Spanish Courses & Classes in Denver, SAT Courses & Classes in San Diego

Popular Test Prep

ACT Test Prep in Denver, SSAT Test Prep in Los Angeles, LSAT Test Prep in Phoenix, GMAT Test Prep in Philadelphia, GRE Test Prep in Philadelphia, ACT Test Prep in Atlanta, GMAT Test Prep in Los Angeles, ACT Test Prep in Los Angeles, GMAT Test Prep in Boston, ISEE Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #15 : Quadratic Formula

Example Question #11 : Quadratic Formula

Example Question #475 : Intermediate Single Variable Algebra

Example Question #476 : Intermediate Single Variable Algebra

Example Question #311 : Quadratic Equations And Inequalities

Example Question #2 : How To Use The Quadratic Function

Example Question #311 : Quadratic Equations And Inequalities

Example Question #481 : Intermediate Single Variable Algebra

Example Question #482 : Intermediate Single Variable Algebra

Example Question #483 : Intermediate Single Variable Algebra

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: