About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Master Solving Quadratic Equations by Completing the Square

Grade 11 Math: Master Advanced Concepts & Skills

11FA.A1.1

auto-gen

Characteristics of quadratic functions

Applications of quadratic functions

11FA.A1.2

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Multiplying polynomial by polynomial

11FA.A1.3

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

11FA.A1.4

Solving quadratic equations by factoring

11FA.A1.5

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

11FA.A1.6

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

11FA.A1.7

Nature of roots of quadratic equations: The discriminant

11FA.A1.8

Solving quadratic equations by completing the square

Applications of quadratic equations

11FA.A2.1

Identifying functions

Function notation

11FA.A2.2

Function notation (advanced)

11FA.A2.3

Domain and range of a function

11FA.A2.4

Introduction to quadratic functions

11FA.A2.5

Transformations of quadratic functions

11FA.A2.6

Combining transformations of functions

11FA.A2.7

Converting from general to vertex form by completing the square

11FA.A2.8

Completing the square

Completing the Square

11FA.A2.9

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

11FA.B1.1

Exponents: Rational exponents

Convert between radicals and rational exponents

11FA.B1.2

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Combining the exponent rules

11FA.B1.3

Graphing exponential functions

11FA.B1.4

Graphing transformations of exponential functions

11FA.B1.5

Finding an exponential function given its graph

11FA.B2.1

Exponential growth and decay by a factor

11FA.B2.2

Evaluating logarithms using change-of-base formula

Solving exponential equations using exponent rules

11FA.B3.1

Exponential growth and decay by percentage

11FA.B3.2

Exponential decay: Half-life

11FA.B3.3

Finance: Compound interest

Finance: Compound Interest

11FA.C1.1

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

11FA.C1.2

Combination of SohCahToa questions

11FA.C1.3

Law of sines

Ambiguous case: SSA triangles

Law of cosines

11FA.C1.4

Applications of the sine law and cosine law

11FA.C1.5

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

11FA.C2.1

Sine graph: y = sin x

11FA.C2.2

Cosine graph: y = cos x

11FA.C2.3

Tangent graph: y = tan x

11FA.C2.4

Cotangent graph: y = cot x

11FA.C2.5

Secant graph: y = sec x

11FA.C2.6

Cosecant graph: y = csc x

11FA.C2.7

Graphing transformations of trigonometric functions

11FA.C3.1

Determining trigonometric functions given their graphs

11FA.C3.2

Ferris wheel trig problems

11FA.C3.3

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

<p>Aligned with your class and textbook, our comprehensive Grade 11 math help covers all topics that you would expect in any typical grade 11 math classes, whether it&apos;s <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grade11.html">Ontario math curriculum</a>, <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/framework_9-12/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=precalc20">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces.</p>

<p>Our video lessons walk you through all topics in trigonometry like Unit circle, Factoring trinomials, Radicals, Rational expressions, Quadratic equations, Sequences and series, and so many more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest math problems. Then, reinforce your understanding with tons of grade 11 math practice.</p>

<p>All our lessons are taught by experienced Grade 11 Math teachers. Let&apos;s finish your homework in no time, and ACE that final.</p>

Grade 11 Functions and Applications, University/College Preparation (MCF3M)

A. Quadratic Functions

B. Exponential Functions

C. Trigonometric Functions

math

<h2>Is grade 11 math hard?</h2>
<p>Grade 11 math can be a struggle and will definitely put your math skills to the test. This can make it seem like grade 11 math is hard and overwhelming. But fear not &ndash; here at StudyPug we&apos;ve made sure to address all your questions and concerns! From topics such as quadratic functions to Sigma notation, down to unraveling the Vertex formula, (and even more!) we&apos;re here to provide you help with grade 11 math. Our carefully crafted Grade 11 math tutorials are well suited for all &ndash; so whether you are a student that requires a refresher on fundamentals or a keener looking to get ahead of the game, we have content covering Grade 11 math for dummies as well as more advanced, challenging content. Regardless of the level of difficulty, we&apos;re here to help you every step of the way with step-by-step examples and lots of practice questions. Grade 11 Math does not have to be hard folks! With help from our review lessons and methodical-disciplined practice, you&apos;ll find yourself powering through the difficult questions with ease and confidence in no time!</p>

<h2>How to prepare for grade 11 math?</h2>
<p>Feeling unprepared for another year of math? Unsure about how and where to get started with grade 11 math? StudyPug has all the tools and resources for you to get you prepared and equipped for grade 11 math!</p>
<p>Understanding grade 11 math will take time and that can be difficult if you only see your tutor once a week or feel like you need a refresher on topics previously covered in class. Here at StudyPug our Grade 11 math tutors and all of our content are readily at your disposal whenever you need them. With 24/7 help and 1000&apos;s of lessons at your fingertips, we are here to help you exercise your understanding of grade 11 math topics and prepare for your upcoming Grade 11 math test and/or Grade 11 math exam preparation. Still feeling like you need more support and background information on some of the topics covered in grade 11 math? Some of the topics you are learning in Grade 11 math (e.g. Quadratic relations, completing the square) we started introducing in <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math</a>. <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math</a> is a prerequisite course for Grade 11 math and we strongly recommend a strong command of the knowledge and skills learned in Grade 10 to help you succeed in Grade 11 math. Head over to our <a href='[[region_textbook.html|{"textbook_key":"grade10"}]]'>Grade 10 math page</a> to begin your revision now!</p>

<h2>How do I use StudyPug to study Grade 11 Math?</h2>
<p>Our intention for StudyPug was to create a 24/7, online companion to meet all your Grade 11 math tutoring needs. We&apos;ve carefully designed our website to be intuitive and easy to navigate but we&apos;ve also included this section for those of you that are visiting or trying us out for the first time. Keep in mind that if you are a student that is still unsure about whether StudyPug is for you, you can still sample our product/service by beginning with the free lessons that are accessible immediately without hassle.</p>
<p>As a general guideline, before jumping into any of our topics in grade 11 math, we recommend starting with assessing your prior knowledge. This is simply done by reviewing your familiarity with concepts we believe you should have a relatively strong command of. Almost all of our topics begin with an outline on the basic concepts you should know as well as other related, pertinent concepts.</p>
<p>If you know exactly what you are looking for, we recommend jumping straight to using our search engine tool. Use this to hone in on the concepts, topics, or questions you are finding the most difficult. Remember; don&apos;t be afraid if you feel like you need to begin with some of the rudimentary foundations you covered previously in grade 10 math or elsewhere.</p>
<p>Once you have identified the topic you require more work on, our short but informative video lessons wills walk you through examples (from easy to complex problems) to flesh out the concepts you need to learn as well as study tips and strategies. Watch and re-watch these lessons as many times as you need! We also provide a paraphrased transcript on the gist of what was addressed in the video if you prefer to learn and revise this way instead.</p>
<p>Last but certainly not the least of these steps, we encourage you to put your knowledge and skills to the test! We&apos;ve prepared plenty of questions per topic for you to master and perfect! See how well you have learnt and acquire more practice from a wide variety and range (i.e. easy to hard) of questions.</p>
<p>Looking for a more entertaining read and method to learn some grade 11 math? <a href="https://www.studypug.com/blog/beauty-and-the-beast/">Swing by our blog to learn about the fibonacci sequence and Kim Kardashian!</a></p>

<h2>How to pass 11th grade math?</h2>
<p>Preparing for a grade 11 Math test or exam? You&apos;ve come to right place! Our home page <a href='[[region_textbook.html|{"textbook_key":"grade11"}]]'>https://www.studypug.com/ca/grade11</a> has everything you need to learn Grade 11 Math. Here at StudyPug we exist to help you achieve your academic goals. So whether you are gearing up for a chapter test on the unit circle or require a quick overview of several topics for your big final exam, we want to make sure you are feeling confident in tackling all your assessments.</p>
<p>At StudyPug we provide numerous Grade 11 math lessons spanning multiple provincial, and international curriculums. We also build content around several renowned textbooks, so we&apos;re well on our way to helping you focus on the numerous topics and types of questions you may be struggling with in 11th grade math.</p>
<p>Remember this &ndash; learning and preparing to pass 11th grade math will not happen overnight! So do not fret if you are finding certain chapters or problems more challenging than others. The key is to first ensure a strong grasp of the underlying concepts and then get into the habit of exercising your knowledge through practice. With over 290 unique practice questions in total for 11th grade math, we readily supplement your classroom learning with the objective of not to merely pass 11th grade math, but to also obtain excellent grades while in the process. Our inventory of practice questions is available to you immediately and should make easy practice out of 11th grade math questions.</p>

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade11math.png

Intro

When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation. 

Solve quadratic equation by completing the square

Factoring perfect square trinomials: <i>(a + b)^2 = a^2 + 2ab + b^2</i> or <i>(a - b)^2 = a^2 - 2ab + b^2</i>