We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Advanced Geometry : How to graph a quadratic function

Study concepts, example questions & explanations for Advanced Geometry

Create An Account

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #161 : Advanced Geometry

What is the range for f(x) below?

$f(x)=-3(x-5)^{2}+7$

Possible Answers:

$y\geq 5$

$y\leq5$

$y\geq 7$

$y\leq7$

Correct answer:

$y\leq7$

Explanation:

$The\ -3\ at\ the\ beginning\ of\ the\ function\ determines\ if\ the\ graph\ opens\ up\ or\ down.$

$The\ parabola\ will\ open\ up\ if\ this\ value\ is\ positive.$

$The\ parabola\ will\ open\ down\ if\ this\ value\ is\ negative.$

$This\ parabola\ opens\ down\ which\ means\ the\ y-value\ of\ the\ vertex\ is\ the\ highest\ point.$

$This\ quadratic\ is\ in\ vertex\ form: f(x)=a(x-h)^{2}+k$

$The\ k\ value\ is\ the\ y-value\ of\ the\ vertex\ which\ is\ 7.$

$Given\ that\ the\ parabola\ opens\ down\ and\ the\ y-value\ of\ the\ vertex\ is\ 7,$

$the\ RANGE\ must\ be\ \mathbf{y\leq 7}.$

Report an Error

Example Question #162 : Advanced Geometry

Find the -intercept and range for the function:

$f(x)=5(x+3)^{2}-4.$

Possible Answers:

$Range: y\leq -4, y-int: (0,41)$

$Range: y\geq-4, y-int: (0,41)$

$Range: y\geq-4, y-int: (0,-4)$

$Range: y\leq -4, y-int: (0,-4)$

Correct answer:

$Range: y\geq-4, y-int: (0,41)$

Explanation:

$The\ range\ for\ a\ quadratic\ is\ determined\ from\ the\ y-value\ of\ the\ vertex.$

$This\ equation\ is\ written\ in\ vertex\ form: y=a(x-h)^{2}+k$

$The\ k -value\ is\ the\ y-coordinate\ for\ the\ vertex.$

$For\ this\ function\ y=5(x+3)^{2}-4,\ the\ k\ value\ is -4.$

$We\ can\ also\ see\ from\ the\ a-value,\ which\ is\ positive\ 5,\ that\ this\ parabola\ will\ open\ up\ on\ the\ graph.$

$\\Both\ of\ these\ together\ give\ us\ the\ range\ which\ is\ y\geq-4.\ It\ is \geq\ because\ the\ parabola\ opens\ up.$

$To\ find\ the\ y-intercept,\ you\ must\ plug\ in\ x=0\ to\ the\ original\ equation.$

$y=5(0+3)^{2}-4$

$Pay\ attention\ to\ order\ of\ operations\ by\ squaring\ the\ (-3)\ before\ multiplying\ by\ 5.$

$After\ simplifying\ we\ get\ y=41\ which\ is\ the\ y-intercept.$

Report an Error

Example Question #71 : Graphing

Find the equation based on the graph shown below:

Screen shot 2015 10 21 at 3.40.06 pm

Possible Answers:

y=x^2+x-12

y=x^2+7x+12

y=x^2-x-12

y=x^2-7x+12

y=x^2-4

Correct answer:

y=x^2-x-12

Explanation:

When you look at the graph, you will see the x-intercepts are

(4,0)(-3,0)

and the y-intercept is

(0,-12) .

These numbers are the solutions to the equation.

You can work backwards and see what the actual equation will come out as,

y=(x-4)(x+3) .

This would distribute to

y=x^2-4x+3x-12

and then simplify to

y=x^2-x-12 .

This also would show a y-intercept of (0,-12) .

Report an Error

Example Question #71 : Graphing

$Find\ the\ vertex\ for\ the\ function: f(x)=4x^{2}-16x+11.$

Possible Answers:

(0,11)

(-2,59)

(2,-5)

(4,-16)

Correct answer:

(2,-5)

Explanation:

$Use \frac{-b}{2a}\ to\ calculate\ the\ x-value\ of\ the\ vertex.$

$\small Given\ the\ function\ f(x)=4x^{2}-16x+11\ is\ in\ standard\ form\ y=ax^{2}+bx+c$

$\small We\ can\ see\ that\ a=4, b=-16\ and\ c=11$

$\small Substitute\ these\ values\ in\ for\ x=\frac{-b}{2a}\ to\ get\ x=\frac{16}{8}=2$

$\small Now\ substitute\ x=2\ into\ the\ function\ f(x)\ to\ get:$

$\small f(2)=4(2)^{2}-16(2)+11=-5$

$\small The\ coordinates\ of\ the\ vertex\ are\ (2,-5)$

Report an Error

Example Question #71 : Coordinate Geometry

Determine the domain and range for the graph of the below function:

f(x)=-3x^2

Possible Answers:

$Domain:\mathbb{R}\and\ Range: y\geq-3$

$Domain:\mathbb{R}\and\ Range: y\leq0$

$Domain:\mathbb{R}\and\ Range: y\leq-3$

$Domain:\mathbb{R}\and\ Range: y\geq0$

Correct answer:

$Domain:\mathbb{R}\and\ Range: y\leq0$

Explanation:

When finding the domain and range of a quadratic function, we must first find the vertex.

$To\ find\ the\ vertex\ of\ a\ quadratic\ we\ must\ first\ find\ the\ x-coordinate\ using\ the\ formula:$

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

$We\ are\ given\ f(x)=-3x^2$

$This\ gives\ us\ an\ a-value\ of\ -3\ while\ b\ and\ c\ both\ equal\ 0.$

$Plugging\ these\ values\ in\ give\ us\ an\ x-coordinate\ and\ y-coordinate\ of\ 0.$

$The\ domain\ of\ all\ quadratics\ is\ ALL\ REAL\ NUMBERS\ (\mathbb{R})$

$With\ a\ negative\ a-value\ we\ know\ this\ quadratic\ opens\ down:$

$so\ the\ range\ is\ y\leq0$

Report an Error

Example Question #72 : Coordinate Geometry

Give the -coordinate(s) of the -intercept(s) of the graph of the function

$f(x)= x^{2}-3x-10$ .

Possible Answers:

-5, 2

The graph of f(x) has no -intercept.

-2, 5

-10, 1

-1, 10

Correct answer:

-2, 5

Explanation:

The -intercept(s) of the graph of f(x) are the point(s) at which it intersects the -axis. The -coordinate of each is 0; their -coordinate(s) are those value(s) of for which f(x) = 0 , so set up, and solve for , the equation:

f(x)= 0

$x^{2}-3x-10 = 0$

To solve this quadratic equation, first, factor the quadratic trinomial as

(x+a)(x+b)

by finding two integers with sum and product . From trial and error, we find the integers and 2, so the equation can be rewritten as

(x-5)(x+2) = 0

By the Zero Factor Principle, one of these two binomials is equal to 0, so either

x-5 = 0 ,

in which case

x = 5 ,

x+2 = 0 ,

in which case

x= -2 .

The graph has two -intercepts at the points (-2, 0) and (5, 0) .

Report an Error

Example Question #71 : Graphing

Give the domain of the function $f(x) = x^{2} + 4x - 17$ .

Possible Answers:

The set of all real numbers

$\left \{ x | x >0 \right \}$

$\left \{ x | x > -17 \right \}$

$\left \{ x | x > -21 \right \}$

$\left \{x| x \ge -2\right \}$

Correct answer:

The set of all real numbers

Explanation:

f(x) is a polynomial function, and as such has the set of all real numbers as its domain.

Report an Error

Example Question #171 : Advanced Geometry

Give the range of the function $f(x) = x^{2} + 4x - 17$ .

Possible Answers:

$\left \{y| y \ge 0 \right \}$

The set of all real numbers.

$\left \{y| y \ge -17 \right \}$

$\left \{y| y \ge -2 \right \}$

$\left \{y| y \ge -21 \right \}$

Correct answer:

$\left \{y| y \ge -21 \right \}$

Explanation:

f(x) is a quadratic function.

One way to find the maximum or minimum value of a quadratic function such as f(x) is to find the vertex of its parabola; its -coordinate will be the one extremum of the range. Whether it is the minimum or maximum value depends on the quadratic coefficient; since it is a positive value here (1), it will be a minimum value.

Set and equal to quadratic and linear coefficients 1 and 4, respectively, and evaluating the expression $-\frac{b}{2a}$ :

$-\frac{b}{2a} = -\frac{4}{2(1)}=-2$

This gives the -coordinate of the vertex; the -coordinate, and the minimum value of f(x) , can be found by evaluating f(-2) , which is done by substitution:

$f(x) = x^{2} + 4x - 17$

$f(-2) = (-2)^{2} + 4(-2) - 17$

=4 + (-8) - 17

= -21

The range is therefore $\left \{y| y \ge -21 \right \}$ .

Report an Error

Example Question #81 : Graphing

Give the -coordinate of the -intercept of the graph of the function

$f(x)= x^{2}-3x-10$

Possible Answers:

The graph of f(x) has no -intercept.

Correct answer:

Explanation:

The -intercept of the graph of f(x) is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is f(0) , which can be found by substituting 0 for in the definition:

$f(x)= x^{2}-3x-10$

$f(0)= 0^{2}-3 \cdot 0-10 = 0 - 0 + 10 = 10$ ,

the correct choice.

Report an Error

← Previous 1 2 3 Next →

View Tutors

Christian
Certified Tutor

North Central College, Bachelor of Science, Physics. University of Wisconsin-Milwaukee, Master of Science, Physics.

View Tutors

Geoffrey
Certified Tutor

University of Vermont, Bachelor of Science, Exercise Science. Virginia Commonwealth University, Masters in Education, Special...

View Tutors

Emmanuel
Certified Tutor

Boise State University, Bachelor of Science, Respiratory Therapy. Duke University, Master of Science, Physician Assistance.

All Advanced Geometry Resources

6 Diagnostic Tests 57 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Atlanta, Chemistry Tutors in San Diego, Physics Tutors in Phoenix, Physics Tutors in Denver, Algebra Tutors in Miami, GRE Tutors in San Diego, Biology Tutors in Seattle, Statistics Tutors in Miami, Calculus Tutors in Washington DC, SSAT Tutors in San Diego

Popular Courses & Classes

Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Denver, ISEE Courses & Classes in Los Angeles, MCAT Courses & Classes in Los Angeles, SAT Courses & Classes in New York City, ACT Courses & Classes in Seattle, Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Phoenix, SSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Miami

Popular Test Prep

ISEE Test Prep in Houston, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Washington DC, GMAT Test Prep in Chicago, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Houston, LSAT Test Prep in Miami, SSAT Test Prep in Phoenix, MCAT Test Prep in Phoenix, ACT Test Prep in Washington DC

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

Advanced Geometry : How to graph a quadratic function

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #161 : Advanced Geometry

Example Question #162 : Advanced Geometry

Example Question #71 : Graphing

Example Question #71 : Graphing

Example Question #71 : Coordinate Geometry

Example Question #72 : Coordinate Geometry

Example Question #71 : Graphing

Example Question #171 : Advanced Geometry

Example Question #81 : Graphing

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: