homework 3 quadratic roots

Solving Quadratic Equations: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

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Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

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Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.

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Quadratic Equations Square Root Worksheets - Download free PDFs

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Solving Quadratic Equations by Taking Square Roots Worksheets

Unlike the standard form: ax 2 + bx + c = 0, most of the quadratic equations offered in this pack of printable high school worksheets have no middle term. Such equations are known as pure quadratic equations and are of the form ax 2 - c = 0. Solving these quadratic equations is made a lot easier by by taking square roots. Let's now get into the process! Here’s all you have to do. Isolate the leading term on the left-hand side of the equation and the constant term on the right-hand side, take square roots on both sides, and simplify both sides for the values of x. The equations that have the middle term can also be solved by finding square roots. Yet again, the middle term is excluded by using the appropriate algebraic identities. Get started with our free worksheet!

Solve Quadratic Equations by Taking Square Roots - Level 1

Push-start your practice of finding the real and complex roots of quadratic equations with this set of pdf worksheets presenting 30 pure quadratic equations. Note that the coefficient of the leading term is 1 in every equation. Hence, simply rewrite the given equation in the form of x 2 = c, and proceed to solve for x.

• Download the set

Solve Quadratic Equations by Taking Square Roots - Level 2

Keep one jump ahead of your peers with this printable practice set perfect for high school students! The quadratic equations here involve integers and fractions. You need to rewrite the equation to the desired form, isolate the x 2 term, take square roots, and perform simplification on both sides.

Related Worksheets

» Solving Equations | Completing the Squares

» Solving Quadratic Equations | Factoring

» Solving Equations | Quadratic Formula

» Sum and Product of the Roots

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Unit 8 – Radicals and the Quadratic Formula

Square Root Functions

LESSON/HOMEWORK

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

Solving Square Root Equations

The Basic Exponent Properties

Fractional Exponents Revisited

More Exponent Practice

The Quadratic Formula

More Work with the Quadratic Formula

Unit Review

Unit #8 Review – Radicals and the Quadratic Formula

UNIT REVIEW

EDITABLE REVIEW

Unit 8 Assessment Form A

EDITABLE ASSESSMENT

Unit 8 Assessment Form B

Unit 8 Assessment Form C

Unit 8 Assessment Form D

Unit 8 Exit Tickets

Unit 8 – Mid-Unit Quiz (Through Lesson #4) – Form A

Unit 8 – Mid-Unit Quiz (Through Lesson #4) – Form B

Unit 8 – Mid-Unit Quiz (Through Lesson #4) – Form C

Unit 8 Mid-Unit Quiz (Through Lesson #4) – Form D

U08.AO.01 – Lesson 2.5 – A Closer Look at Extraneous Roots

EDITABLE RESOURCE

U08.AO.02 – Deriving the Quadratic Formula (Enrichment)

U08.AO.03 – Additional Practice with Exponents and Roots

U08.AO.04 – Quadratic Formula Practice

U08.AO.05 – Practice with Completing the Square vs the Quadratic Formula

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Quadratic Equation Solver

What do you want to calculate.

• Solve for Variable
• Practice Mode
• Step-By-Step

Step-By-Step Example

Example (click to try), choose your method, solve by factoring.

Example: 3x^2-2x-1=0

Complete The Square

Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.)

Take the Square Root

Example: 2x^2=18

Quadratic Formula

Example: 4x^2-2x-1=0

About quadratic equations

Need more problem types? Try MathPapa Algebra Calculator

Clear Quadratic Equation Solver »

Quadratic equation root calculator

Want to calculate? Get Solutions Here:

Enter a math problem on an Equation in the text area Above

Example x^2-2x+3=4 -OR- 2x-y=9 Click the button to Solve!

Graphical Solution of Equations:

A worked example to illustrate how the quadratic calculator works:.

This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation. A quadratic is a second degree polynomial of the form: ax^2+bx+c=0 where a\neq 0 . To solve an equation using the online calculator, simply enter the math problem in the text area provided. Hit the calculate button to get the roots. A quadratic equation has two roots or zeroes namely; Root1 and Root2.

An equation root calculator that shows steps

Learning math with examples is the best approach. With our online calculator, you can learn how to find the roots of quadratics step by step. First, find the roots or solutions your way, and then use the roots calculator to confirm your answer. The calculator uses the quadratic formula to find the roots of a quadratic equation.

Solved quadratic equation examples

x^2 -6x + 3 = 0

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

x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(1)(3)}}{ 2(1) }

x = \dfrac{ 6 \pm \sqrt{36 - 12}}{ 2 }

x = \dfrac{ 6 \pm \sqrt{24}}{ 2 }

  x = \frac{ 6 \pm 2 \sqrt{6}}{ 2 }

x = = 3+\sqrt{6} Or x = 3- \sqrt{6}

Need to learn Algebra through examples?

Find more quadratic formula calculator Solved Examples Here:

How the Quadratic formula root calculator works

The online roots calculator is simple to use. Furthermore, the calculator can be used to find roots of varied problems. Whether the roots are real or complex, the calculator is able show a step by step solution.

To use this calculator, Insert your math expression on the textarea provided. Note you should only use the allowed notations and characters in order to obtain correct solution. Once you have the right expression or equation, Hit the calculate button to get started. The calculator will show you all the steps together with the reasoning or explanation behind each of the steps.

Acceptable Math symbols and their usage If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators.

• + Used for Addition
• - Used for Subtraction
• * multiplication operator symbol
• / Division operator
• ^ Used for exponent or to Raise to Power
• sqrt Square root operator

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Quadratic Equations (Algebra 1 Curriculum - Unit 8) | All Things Algebra®

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Description

This Quadratic Equations Unit Bundle contains guided notes, homework assignments, four quizzes, study guide and a unit test that cover the following topics:

• Introduction to Quadratic Equations (Standard Form, Vertex, Axis of Symmetry, Maximum, Minimum)

• Graphing Quadratic Equations by Table (Review of Domain/Range included)

• Vertex Form and Transformations

• Quadratic Roots (Identifying by Graphing)

• The Discriminant

• Solving Quadratic Equations by Factoring

• Solving Quadratic Equations by Square Roots

• Solving Quadratic Equations by Completing the Square

• Solving Quadratic Equations by the Quadratic Formula

• Review of all Methods

• Applications: Area and Consecutive Integers

• Projectile Motion

• Linear vs. Quadratic Models

ADDITIONAL COMPONENTS INCLUDED:

(1) Links to Instructional Videos: Links to videos of each lesson in the unit are included. Videos were created by fellow teachers for their students using the guided notes and shared in March 2020 when schools closed with no notice.  Please watch through first before sharing with your students. Many teachers still use these in emergency substitute situations. (2) Editable Assessments: Editable versions of each quiz and the unit test are included. PowerPoint is required to edit these files. Individual problems can be changed to create multiple versions of the assessment. The layout of the assessment itself is not editable. If your Equation Editor is incompatible with mine (I use MathType), simply delete my equation and insert your own.

(3) Google Slides Version of the PDF: The second page of the Video links document contains a link to a Google Slides version of the PDF. Each page is set to the background in Google Slides. There are no text boxes;  this is the PDF in Google Slides.  I am unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead! 

Please download the preview to see a sample outline along with a collage of some of the pages.

This resource is included in the following bundle(s):

Algebra 1 Second Semester Notes Bundle

Algebra 1 Curriculum Algebra 1 Curriculum (with Activities)

More Algebra 1 Units:

Unit 1 – Algebra Basics

Unit 2 – Multi-Step Equations & Inequalities

Unit 3 – Relations & Functions

Unit 4 – Linear Equations

Direct & Inverse Variation (Mini-Unit)

Unit 5 – Systems of Equations & Inequalities

Unit 6 – Exponents and Exponential Functions

Unit 7 – Polynomials & Factoring

Unit 9 – Linear, Quadratic, and Exponential Functions

Unit 10 – Radical Expressions & Equations

Unit 11 – Rational Expressions & Equations

Unit 12 – Statistics

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable , meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at [email protected].

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

© All Things Algebra (Gina Wilson), 2012-present

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