Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

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 #461 : Intermediate Single Variable Algebra

A baseball that is thrown in the air follows a trajectory of h(t)= -4t^2 +12t+6 , where h(t) is the height of the ball in feet and is the time elapsed in seconds. How long does the ball stay in the air before it hits the ground?

Possible Answers:

Between 2 and 2.5 seconds

Between 4 and 4.5 seconds

Between 3.5 and 4 seconds

Between 3 and 3.5 seconds

Between 2.5 and 3 seconds

Correct answer:

Between 3 and 3.5 seconds

Explanation:

To solve this, we look at the equation h(t)=0 .

Setting the equation equal to 0 we get 0= -4t^2 +12t+6 .

Once in this form, we can use the Quadratic Formula to solve for .

The quadratic formula says that if 0= -ax^2 +bx+c , then

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

Plugging in our values:

$t= \frac{-12\pm\sqrt{(12^2-4(-4)(6)}}{2(-4)}=\frac{-12\pm \sqrt{240}}{-8}= \frac{12\pm15.5}{8}$

Therefore t=3.4375 or -.4375 and since we are looking only for positive values (because we can't have negative time), 3.4375 seconds is our answer.

Report an Error

Example Question #4 : Quadratic Formula

Use the quadratic formula to solve the following equation.

4x^2 -12x + 20 = 4

Possible Answers:

$x = \frac{3 \pm \sqrt{7}i}{2}$

$x = \frac{-3 \pm \sqrt{7}i}{2}$

$x = \left \{ -1, 4\right \}$

$x = \frac{-3 \pm \sqrt{7}}{2}$

$x = \frac{3 \pm \sqrt{7}}{2}$

Correct answer:

$x = \frac{3 \pm \sqrt{7}i}{2}$

Explanation:

First we want to put the equation into standard form; we do this by making sure the equation is = 0, so let's subtract 4 from both sides.

4x^2 -12x + 20 = 4

4x^2 -12x + 20 -4= 4-4

4x^2 -12x + 16 = 0

We could go straight to the quadratic formula from here, but quadratics are always easier to solve if we eliminate Greatest Common Factors first. In this case the GCF is 4 so let's divide both sides by 4.

$\frac{4x^2 -12x + 16}{4} = \frac{0}{4}$

x^2 -3x + 4 = 0

Now we can compare against the standard form to find a, b, and c.

ax^2 -bx + c = 0

x^2 -3x + 4 = 0

By pattern matching, we see that a = 1, b = -3, and c = 4. Now we substitute into the quadratic formula.

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

$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(4)}}{2(1)}$

$x = \frac{3 \pm \sqrt{9 - 16}}{2}$

$x = \frac{3 \pm \sqrt{-7}}{2}$

We can evaluate the square root of a negative number by factoring out the square root of -1 and calling it the imaginary number i. This gives our answer.

$x = \frac{3 \pm \sqrt{7}*\sqrt{-1}}{2}$

$x = \frac{3 \pm \sqrt{7}i}{2}$

Report an Error

Example Question #2 : Quadratic Formula

Use the quadratic formula to solve the following equation:

2x^2 + 4x -3 =0

Possible Answers:

$x = \frac{-2 \pm\sqrt{10}}{2}$

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

$x = -1 \pm\sqrt{10}$

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

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

Correct answer:

$x = \frac{-2 \pm\sqrt{10}}{2}$

Explanation:

Since the equation is already in standard form, we can compare it to the general version of standard form to find a, b, and c.

ax^2 + bx + c = 0

2x^2 +4x -3 = 0

By pattern matching it is clear that a = 2, b = 4, and c = -3. Now we can substitute into the quadratic formula.

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

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

Recall that when subtracting a negative number [as in - 4(2)(-3)], the result is addition:

$x =\frac{-4 \pm\sqrt{16 + 24}}{4}$

Combine terms and simplify the radical:

$x =\frac{-4 \pm\sqrt{40}}{4}$

$x =\frac{-4 \pm\sqrt{4}*\sqrt{10}}{4}$

$x =\frac{-4 \pm\2\sqrt{10}}{4}$

Now eliminate common factors to reduce to lowest terms.

$x =\frac{-2(2) \pm\(2)\sqrt{10}}{2(2)}$

$x =\frac{-2 \pm\sqrt{10}}{2}$

Report an Error

Example Question #2 : Quadratic Formula

Use the quadratic formula to find the solutions of the following equation:

2x^2 -3x - 5 = 0

Possible Answers:

$x = \frac{3 \pm 7i}{4}$

$x = \left \{ -1, \frac{5}{2}\right \}$

$x=\left \{ -2, 5\right \}$

$x = \left \{ -\frac{5}{2}, 1\right \}$

$x = \frac{3 \pm\sqrt{31}i}{4}$

Correct answer:

$x = \left \{ -1, \frac{5}{2}\right \}$

Explanation:

We begin by designating values of a, b and c by comparing the equation to the standard form.

ax^2 + bx + c = 0

2x^2 - 3x - 5 = 0

By pattern matching it is clear that a = 2, b = -3, and c = -5. We can now substitute into the quadratic formula:

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

$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(-5)}}{2(2)}$

Take note that in the two cases where negatives/minus signs are multiplied together [-(-3) and -4(2)(-5)], they bceome positive:

$x = \frac{3 \pm \sqrt{9 +40}}{4}$

$x = \frac{3 \pm \sqrt{49}}{4}$

Now we simplify and evaluate.

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

$x = \left \{ \frac{3 - 7}{4}, \frac{3+7}{4}\right \}$

Note that in the previous step we listed the subtraction instance first, as that instance yields the smaller number and it is usually convenient to start sets with smaller numbers first.

$x = \left \{ \frac{-4}{4}, \frac{10}{4}\right \}$

$x = \left \{ -1,\frac{5}{2}\right \}$

Report an Error

Example Question #6 : Quadratic Formula

Solve for . Use the quadratic formula to find your solution. Use a calculator to estimate the value to the closest hundredth.

x^2 - 4x + 5 = 0

Possible Answers:

1.23 and -3.11

and

No solution

5.24 and -2.34

2.38 and 39.33

Correct answer:

No solution

Explanation:

Recall that the quadratic formula is defined as:

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

For this question, the variables are as follows:

ax^2+bx+c=0

x^2 - 4x + 5 = 0

a = 1

b = -4

c = 5

Substituting these values into the equation, you get:

$\frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(5)}}{2(1)}$

$\frac{4 \pm \sqrt{16 - 20}}{2}$

$\frac{4 \pm \sqrt{-4}}{2}$

Since you have to take the square root of a negative number, this means that there are no real solutions.

Report an Error

Example Question #3 : Quadratic Formula

Solve for . Use the quadratic formula to find your solution. Use a calculator to estimate the value to the closest hundredth.

x^2 - 7x - 5 = 0

Possible Answers:

5.23 and -4.29

2.39 and -3.48

33.21 and -12.32

7.65 and -0.65

No solution

Correct answer:

7.65 and -0.65

Explanation:

Recall that the quadratic formula is defined as:

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

For this question, the variables are as follows:

ax^2+bx+c=0

x^2 - 7x - 5 = 0

a = 1

b = -7

c = -5

Substituting these values into the equation, you get:

$\frac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(-5)}}{2(1)}$

$\frac{7 \pm \sqrt{49 - (-20)}}{2}$

$\frac{7 \pm \sqrt{49 +20}}{2}$

$\frac{7 \pm \sqrt{69}}{2}$

Use a calculator to determine the final values.

$\frac{7+\sqrt{69}}{2}=7.65$

$\frac{7-\sqrt{69}}{2}=-0.65$

Report an Error

Example Question #8 : Quadratic Formula

Solve for . Use the quadratic formula to find your solution. Use a calculator to estimate the value to the closest hundredth.

x^2 + 5x - 5 = 0

Possible Answers:

4.92 and -2.92

84.21 and 11.92

0.85 and -5.85

No solution

5.23 and -6.53

Correct answer:

0.85 and -5.85

Explanation:

Recall that the quadratic formula is defined as:

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

For this question, the variables are as follows:

ax^2+bx+c=0

x^2 + 5x - 5 = 0

a = 1

b = 5

c = -5

Substituting these values into the equation, you get:

$\frac{-5 \pm \sqrt{(5)^2 - 4(1)(-5)}}{2(1)}$

$\frac{-5 \pm \sqrt{25 +20)}}{2}$

$\frac{-5 \pm \sqrt{45}}{2}$

Use a calculator to determine the final values.

$\frac{-5+\sqrt{45}}{2}=0.85$

$\frac{-5-\sqrt{45}}{2}=-5.85$

Report an Error

Example Question #11 : Quadratic Formula

Solve for . Use the quadratic formula to find your solution. Use a calculator to estimate the value to the closest hundredth.

5x^2 - 17x + 12 = 0

Possible Answers:

17.71 and -6.17

No solution

8.13 and 4.21

and 2.4

1.52 and 3.52

Correct answer:

and 2.4

Explanation:

Recall that the quadratic formula is defined as:

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

For this question, the variables are as follows:

ax^2+bx+c=0

5x^2 - 17x + 12 = 0

a = 5

b = -17

c = 12

Substituting these values into the equation, you get:

$\frac{-(-17) \pm \sqrt{(-17)^2 - 4(5)(12)}}{2(5)}$

$\frac{17 \pm \sqrt{289 - 240}}{10}$

$\frac{17 \pm \sqrt{49}}{10}$

$\frac{17 \pm 7}{10}$

Separate this expression into two fractions and simplify to determine the final values.

$\frac{17 + 7}{10} = \frac{24}{10} = 2.4$

$\frac{17 - 7}{10} = \frac{10}{10} = 1$

Report an Error

Example Question #471 : Intermediate Single Variable Algebra

Solve for . Use the quadratic formula to find your solution. Use a calculator to estimate the value to the closest hundredth.

3x^2 +8x - 11 = 0

Possible Answers:

and -3.67

5.28 and -2.34

9.87 and -6.87

No solution

-3.28 and 2.83

Correct answer:

and -3.67

Explanation:

Recall that the quadratic formula is defined as:

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

For this question, the variables are as follows:

ax^2+bx+c=0

3x^2 +8x - 11 = 0

a = 3

b = 8

c = -11

Substituting these values into the equation, you get:

$\frac{-(8) \pm \sqrt{(8)^2 - 4(3)(-11)}}{2(3)}$

$\frac{-8 \pm \sqrt{64 - (-132)}}{6}$

$\frac{-8 \pm \sqrt{64 +132}}{6}$

$\frac{-8 \pm \sqrt{196}}{6}$

$\frac{-8 \pm 14}{6}$

Separate this expression into two fractions and simplify to determine the final values.

$\frac{-8 + 14}{6} = \frac{6}{6} = 1$

$\frac{-8 - 14}{6} = \frac{-22}{6} = -3.67$

Report an Error

Example Question #471 : Intermediate Single Variable Algebra

Solve the quadratic equation with the quadratic formula.

$2x^{2}+3x-1=0$

Possible Answers:

$x=\frac{-3\pm\sqrt{1}}{4}$

$x=\frac{-3\pm\sqrt{17}}{4}$

$x=\frac{-3\pm\sqrt{17}}{2}$

$x=-\frac{1}{2},-1$

$x=\frac{3\pm\sqrt{17}}{4}$

Correct answer:

$x=\frac{-3\pm\sqrt{17}}{4}$

Explanation:

Based on the quadratic equation:

$ax^{2}+bx+c=0$ ,

a=2 , b=3 , and c=-1

Given the quadratic formula:

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

We have:

$x=\frac{-3\pm \sqrt{3^{2}-4(2)(-1)}}{2(2)}$

Simplfying,

$x=\frac{-3\pm\sqrt{17}}{4}$

Report an Error

View Algebra 2 Tutors

Robert
Certified Tutor

University of Pittsburgh, Bachelor of Science, Physics.

View Algebra 2 Tutors

Mohammad
Certified Tutor

Jamia Millia Islamia, Master of Science, Physics.

View Algebra 2 Tutors

Sydney
Certified Tutor

Florida Gulf Coast University, Bachelor of Science, Mathematics.

All Algebra II Resources

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

Popular Subjects

GMAT Tutors in Miami, SAT Tutors in Miami, Chemistry Tutors in Seattle, Algebra Tutors in Phoenix, Statistics Tutors in New York City, Computer Science Tutors in Houston, Reading Tutors in Atlanta, GRE Tutors in Seattle, Statistics Tutors in Denver, Biology Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Chicago, GRE Courses & Classes in Chicago, SSAT Courses & Classes in Los Angeles, SAT Courses & Classes in San Diego, ISEE Courses & Classes in Boston, SAT Courses & Classes in Chicago, ISEE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

SSAT Test Prep in Atlanta, MCAT Test Prep in Atlanta, ISEE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in Phoenix, GRE Test Prep in Seattle, GMAT Test Prep in Atlanta, ACT Test Prep in Seattle, GMAT Test Prep in New York City, GRE Test Prep in Miami

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 : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #461 : Intermediate Single Variable Algebra

Example Question #4 : Quadratic Formula

Example Question #2 : Quadratic Formula

Example Question #2 : Quadratic Formula

Example Question #6 : Quadratic Formula

Example Question #3 : Quadratic Formula

Example Question #8 : Quadratic Formula

Example Question #11 : Quadratic Formula

Example Question #471 : Intermediate Single Variable Algebra

Example Question #471 : 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: