Call Now to Set Up Tutoring:

(888) 888-0446

Advanced Geometry : Coordinate Geometry

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

Example Question #166 : Coordinate Geometry

Which of the following is the equation of the line of symmetry of a horizontal parabola on the coordinate plane with its vertex at (8,4) ?

Possible Answers:

x= 8

x-2y = 0

x+y = 12

x-y = 4

y = 4

Correct answer:

y = 4

Explanation:

The line of symmetry of a horizontal parabola is a horizontal line, the equation of which takes the form y = b for some . The line of symmetry passes through the vertex, which here is (8,4) , so the equation must be y = 4 .

Report an Error

Example Question #21 : Graphing

The graphs of the functions f(x) and g(x) have the same -intercept.

If we define $f(x) = 2x^{2}+ 4x+7$ , which of the following is a possible definition of g(x) ?

Possible Answers:

$g(x) = 6x^{2}+ 3x-7$

$g(x) = x^{2}+ 2x+6$

$g(x) =4x^{2}+ 16x+14$

$g(x) = 4x^{2}+ 8x+7$

$g(x) = -2x^{2}- 4x-14$

Correct answer:

$g(x) = 4x^{2}+ 8x+7$

Explanation:

The -coordinate of the -intercept of the graph of a function of the form $f(x)= Ax^{2}+Bx+C$ - a quadratic function - is the point (0, f(0)) . Since $f(x)= A \cdot 0^{2}+B \cdot 0 +C = C$ , the -intercept is at the point (0,C) .

Because of this, the graph of $f(x) = 2x^{2}+ 4x+7$ has its -intercept at (0,7) . Among the other choices, only $g(x) = 4x^{2}+ 8x+7$ has a graph with its -intercept also at (0,7) .

Report an Error

Example Question #71 : Coordinate Geometry

Find the vertex and determine if the vertex is a maximum or minimum for below.

$f(x)=-x^{2}+2x-8$

Possible Answers:

Vertex: (1,-5), Max

Vertex: (1,-7), Min

Vertex: (1,-7), Max

Vertex: (1,-5), Min

Correct answer:

Vertex: (1,-7), Max

Explanation:

The correct answer for the vertex is found by first finding the x of the vertex:

$x=\frac{-b}{2a}\ where\ a=-1\ and\ b=2$

Plug in a and b to get:

$x=\frac{-2}{2(-1)}=\boldsymbol{\mathit{}1}$

To find the y value of the vertex, plug in what was found for x above in the original f(x).

$f(x)=-x^{2}+2x-8\ plug\ in\ x=1$

$f(1)=-(1)^{2}+2(1)-8=\boldsymbol{\mathit{}-7}$

a common mistake here is the order of operations, at the beginning the 1 is squared before it is multipled by the negative out front.

$The\ vertex\ is\ \boldsymbol{\mathbf{\mathit{}}(1,-7)}$

Now we must consider if the vertex is a MAX or a MIN

Since the a value is negative, this means the parabola will open down, which means the vertex is the highest point on the graph.

$The\ vertex\ is\ the\ \boldsymbol{MAX}$

Report an Error

Example Question #161 : Advanced Geometry

What is the range for f(x) below?

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

Possible Answers:

$y\geq 7$

$y\leq7$

$y\leq5$

$y\geq 5$

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:

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

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

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

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

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 #163 : Advanced Geometry

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 #164 : Advanced Geometry

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

Possible Answers:

(-2,59)

(0,11)

(4,-16)

(2,-5)

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 #165 : Advanced Geometry

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

f(x)=-3x^2

Possible Answers:

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

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

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

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

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 #166 : Advanced Geometry

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

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

Possible Answers:

-10, 1

-1, 10

-5, 2

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

-2, 5

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 #72 : Coordinate Geometry

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

Possible Answers:

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

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

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

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

The set of all real numbers

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

View Tutors

Brittany
Certified Tutor

Capella University, Bachelor of Science, Nursing (RN).

View Tutors

David
Certified Tutor

The University of Texas at El Paso, Bachelor of Science, Computational Mathematics. Indiana State University, Master of Scien...

View Tutors

Elizabeth
Certified Tutor

University of Oklahoma Norman Campus, Bachelor of Education, Education. University of Oklahoma Norman Campus, Master of Scien...

All Advanced Geometry Resources

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

Popular Subjects

SSAT Tutors in Chicago, Biology Tutors in Los Angeles, Statistics Tutors in Denver, Algebra Tutors in Boston, Computer Science Tutors in San Francisco-Bay Area, Spanish Tutors in Seattle, Algebra Tutors in Denver, English Tutors in Atlanta, GRE Tutors in Houston, Physics Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Phoenix, ACT Courses & Classes in Atlanta, SSAT Courses & Classes in Miami, SAT Courses & Classes in Miami, Spanish Courses & Classes in Phoenix, SSAT Courses & Classes in Seattle, GRE Courses & Classes in Miami, ACT Courses & Classes in Chicago, GRE Courses & Classes in Seattle, LSAT Courses & Classes in Miami

Popular Test Prep

GMAT Test Prep in Chicago, ACT Test Prep in Phoenix, ACT Test Prep in Chicago, SAT Test Prep in Miami, GRE Test Prep in Miami, ACT Test Prep in Miami, ACT Test Prep in Atlanta, GMAT Test Prep in Seattle, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Los Angeles

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 : Coordinate Geometry

Study concepts, example questions & explanations for Advanced Geometry

All Advanced Geometry Resources

Example Questions

Example Question #166 : Coordinate Geometry

Example Question #21 : Graphing

Example Question #71 : Coordinate Geometry

Example Question #161 : Advanced Geometry

Example Question #162 : Advanced Geometry

Example Question #163 : Advanced Geometry

Example Question #164 : Advanced Geometry

Example Question #165 : Advanced Geometry

Example Question #166 : Advanced Geometry

Example Question #72 : Coordinate Geometry

All Advanced Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: