Solving Quadratic Equations Vocabulary

Equation where the highest exponent is a 2

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Quadratic Equation Solver

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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

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Solving Quadratic Equations

Related Topics: More Lessons for Basic Algebra Math Worksheets

A series of free, online Basic Algebra Lessons.

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Vocabulary of Quadratic Polynomials

Polynomials Quadratic equations and functions have a lot of complex vocabulary that can make them difficult to solve. When solving quadratic polynomials, there are several different ways to instruct students on how to find the roots, find the solutions, find the x-intercepts or find the zeroes of polynomial functions and quadratic graphs. How to label the roots of a quadratic polynomial, solutions to a quadratic equation, and x-intercepts or roots of a quadratic function. Short definitions for Parabola, axis of symmetry, vertex, maximum, minimum, solutions and the discriminant.

Solving Quadratic Equations by Factoring

When we solve quadratic equations, we have several different methods that we can choose from. Solving quadratic equations by factoring is just one of those methods. When solving quadratic equations by factoring, we set one side of the equation to zero and then factor the quadratic equation so that we can use the zero product property to determine where x = 0. Quadratic equations can also be solved by using square roots, completing the square or the quadratic formula.

Solving Quadratic Equations by Factoring - Basic Examples

Solving Quadratic Equations by Factoring - Another Example

Solving Quadratic Equations using Square Roots

Solving quadratics can be difficult and solving quadratics using square roots is just one of the methods of solving a quadratic equation. Solving a quadratic equation using square roots works best when we have a quadratic equation that does not have a “b” term and by taking the square root of either side of the equation. Quadratic equations can also be solved by factoring, completing the square or the quadratic formula.

This video explains how use square roots to solve quadratic equations in the form ax 2 + c = 0.

This video provides examples on how square roots can be used to solve certain types of quadratic equations

Completing the Square

Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by several methods including factoring, graphing, using the square roots or the quadratic formula. Completing the square will always work when solving quadratic equations and is a good tool to have. Solving a quadratic equation by completing the square is used in a lot of word problems.

Completing the Square - Solving Quadratic Equations. This video shows an easier example of completing the square.

Completing the Square - Solving Quadratic Equations. This video shows a slightly harder example of completing the square to solve a quadratic equation.

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In math, quadratic things have something to do with squaring them — in other words, multiplying a number times itself or raising it to the second power.

When you come across a math problem that includes "X squared," it's quadratic. In algebra, it's especially common to use the quadratic equation, which has this form: ax squared plus bx plus c equals 0 . The word quadratic comes up in calculus and statistics, too, and it can also be used to mean "square." In fact, the Latin root quadratus also means "square."

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Quadratic Equations and Functions

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Radical Expressions and Equations

solving quadratic equations vocabulary

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Vocabulary of Quadratic Polynomials - Concept

Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions , we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are trinomials .

Math problems can be tricky if you don't understand the directions. And that's especially tricky when you come to your study of quadratic functions because I'm going to show you four different instructions that essentially mean the same thing. Check it out. Find the roots of the quadratic polynomial f of x equals x squared plus 3x plus 2. If you saw those directions what you would do is set this function equal to zero, factor or use the quadratic formula or complete the square or do graphing choose whatever method you want to to solve this. I'm going to factor because I'm a pretty good factorer. And I get the solutions x=-1 and x=-2 when I use the zero product property. So that's one set of instructions for this problem. Let's look at the same problem with a different set of instructions. Find solutions of the equation. Notice the difference. This was roots of a polynomial. This is solutions of an equation. It's the same mathematical process. I'm still going to go ahead and factor, use the zero product property and I'm going to get the same answers. x=-1, x=-2, go back check your solutions by substituting them in if you want to. That's tricky. Same problem, different words, let's look there's even a third way to do it. Let me back up. What we have here is find the x intercepts of the graph of y=x squared plus 3x plus two. Notice this is the same equation, the same function, the same polynomial only now they're telling me to look for the x intercepts. So if I look on the x intercepts, here is where I get my answers -2 and -1. It's the same answers. What I really I'm trying to show you guys that these four things are all just different instructions for doing the same mathematical process. Roots of polynomials, solutions of equations, intercepts of graphs and we also have zeros of a function. And what would happen with zeros of a function is you would have a function like this, this is the same one we've been working with all along. I'm looking at the table and finding the zeros. Finding the zeros means look for where your y value or in our case we're looking at f of x is equal to zero. Here they are right here. -2 and 1, does that sound familiar? It's the same answer we got all along. So you guys, I understand. Like I'm a Math teacher, I get it. I do all these problems with you. I know the directions can be really tricky and that's why I wanted to try to clarify. These are four different sets of instructions using four different sets of vocabulary pairings that essentially mean the same thing. One thing I want you guys to start thinking about is how they're alike and how they're different, and also thinking about what vocabulary words go together. Graphs goes with x intercepts, roots goes with polynomials, solutions goes with equations. Those kinds of pairings, if you mess them up, people would still understand what you're talking about but formally you want to make sure you have the right match ups when you're doing and talking about your Math problems.

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COMMENTS

  1. Solving Quadratic Equations: Vocabulary Flashcards

    divide b by 2 and square it to find c, and then find the root Square Root quadratic when both sides of the quadratic equation are perfect squares, square root both sides and solve for x Quadratic Formula Method plug in a, b, and c into the quadratic formula and solve If the discriminant is negative, there are complex solutions

  2. Solving Quadratic Equations Vocabulary Flashcards & Practice Test

    Start studying Solving Quadratic Equations Vocabulary. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

  3. Solving Quadratic Equations with Complex Roots

    Solving Quadratic Equations with Complex Roots - Vocabulary and Equations Quadratic Equation: A quadratic equation is an equation of the form ax^2 Show more 7:09 What are all...

  4. PDF Quadratic Functions Vocabulary

    Quadratic Functions Vocabulary Quadratic Function is a polynomial function with the highest degree of 2 for the variable x. It can be written in the form y = ax2 +bx + c. Parabola is the graph of a quadratic function. x-intercepts are the x-values where the parabola intersects the x-axis. y-intercept is the y-value where the parabola intersects the y-axis.

  5. Quadratic Equation Solver

    There are different methods you can use to solve quadratic equations, depending on your particular problem. 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

  6. Quadratic Equation Vocabulary Worksheets & Teaching Resources

    Skills Based Algebra 1 resources for Solving Quadratic Equations Unit. Includes:1 vocabulary level tracker3 leveled vocabulary resources to helps students level up (use 2 as practice and one for supplementing assessment.) 1 Solving Quadratic Equations student skills progress tracker Subjects: Algebra, Math Grades: 8th - 10th Types:

  7. Quadratics Vocabulary Flashcards

    Quadratics Vocabulary Shared Flashcard Set Details Title Quadratics Vocabulary Description This flashcard set helps students learn the necessary vocabulary for Quadratics. Total Cards 8 Subject Mathematics Level 9th Grade Created 03/31/2011 Click here to study/print these flashcards . Create your own flash cards! Sign up here .

  8. Quadratics Vocabulary

    Q. The minimum of a quadratic function is. answer choices. The lowest point (vertex) on a graph when a parabola opens up; the point where the graph changes from decreasing to increasing. The highest point (vertex) on a graph when a parabola opens down; the point where the graph changes from increasing to decreasing.

  9. Solving Quadratic Equations Vocabulary Word Search

    Or even something to leave with a substitute?This download comes with a word search of vocabulary words all about Solving Quadratic Equations and a color coded answer key!Students will need to find 12 vocabulary terms. Those terms include:Completing the SquareDi... More like this Vocabulary Activities Math Worksheets Algebra I Algebraic Expressions

  10. Solving Quadratic Equations and Inequalities

    Solving Quadratic Equations Quadratic Inequalities Vocabulary completing the square process used to rewrite a quadratic expression as the sum of a perfect square trinomial and a constant discriminant part of the quadratic formula that is under the radical sign: b^2-4ac b2 − 4ac factoring

  11. Quadratic equation

    quadratic equation: 1 n an equation in which the highest power of an unknown quantity is a square Synonyms: quadratic Type of: equation a mathematical statement that two expressions are equal

  12. Solving Quadratic Equations

    Vocabulary of Quadratic Polynomials. Polynomials Quadratic equations and functions have a lot of complex vocabulary that can make them difficult to solve. When solving quadratic polynomials, there are several different ways to instruct students on how to find the roots, find the solutions, find the x-intercepts or find the zeroes of polynomial ...

  13. Quadratic

    When you come across a math problem that includes "X squared," it's quadratic. In algebra, it's especially common to use the quadratic equation, which has this form: ax squared plus bx plus c equals 0. The word quadratic comes up in calculus and statistics, too, and it can also be used to mean "square."

  14. How to Solve a Quadratic Equation with Complex Roots

    Solving Quadratic Equations with Complex Roots - Vocabulary and Equations. Quadratic Equation: A quadratic equation is an equation of the form {eq}ax^2 + bx + c = 0 {/eq}, where a, b, and c are ...

  15. Vocabulary of Quadratic Polynomials

    Vocabulary of Quadratic Polynomials - Concept. Adding and subtracting rational expressions is similar to adding fractions. When adding and subtracting rational expressions, we find a common denominator and then add the numerators. To find a common denominator, factor each first. This strategy is especially important when the denominators are ...

  16. Quadratic Equations: Very Difficult Problems with Solutions

    Quadratic Equations: Very Difficult Problems with Solutions. Problem 1. Solve the equation \displaystyle \frac {5} {2-x}+\frac {x-5} {x+2}+\frac {3x+8} {x^2-4}=0 2−x5 + x+2x−5 + x2 −43x+8 = 0. In the answer box, write the roots separated by a comma. Problem 2. If \displaystyle x^2-2ax+a^2=0 x2 −2ax+a2 = 0, find the value of ...