Solving Quadratic Equations Vocabulary


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Solving Quadratic Equations
Related Topics: More Lessons for Basic Algebra Math Worksheets
A series of free, online Basic Algebra Lessons.
In this lesson, we will learn
- vocabulary of quadratic polynomials
- how to solve quadratic equations by factoring
- how to solve quadratic equations using square roots
- how to solve quadratic equations by completing the square
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."
- adjective of or relating to the second power “ quadratic equation”
- adjective of or relating to or resembling a square “ quadratic shapes”
- noun a polynomial of the second degree synonyms: quadratic polynomial see more see less type of: multinomial , polynomial a mathematical function that is the sum of a number of terms
- noun an equation in which the highest power of an unknown quantity is a square synonyms: quadratic equation see more see less type of: equation a mathematical statement that two expressions are equal
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Quadratic Equations and Functions
- Concept 4 min
- Problem 1 3 min
- Problem 2 2 min
- Problem 3 3 min
- Problem 4 4 min
- Problem 5 5 min
- Problem 6 5 min
- Concept 3 min
- Problem 1 5 min
- Problem 2 5 min
- Problem 3 5 min
- Problem 4 5 min
- Problem 5 4 min
- Problem 6 3 min
- Problem 7 4 min
- Problem 8 5 min
- Problem 9 5 min
- Problem 10 5 min
- Problem 11 4 min
- Concept 7 min
- Problem 3 min
- Concept 8 min
- Vocabulary of Quadratic Polynomials 1
- --> Vocabulary of Quadratic Polynomials 3 min
- Concept 2 min
- Problem 1 1 min
- Problem 2 1 min
- Problem 3 1 min
- Problem 4 2 min
- Problem 5 3 min
- Problem 7 3 min
- Problem 8 4 min
- Problem 9 2 min
- Problem 10 4 min
- Problem 11 3 min
- Problem 12 5 min
- Problem 13 3 min
- Problem 14 3 min
- Problem 15 3 min
- Problem 2 3 min
- Problem 5 2 min
- Problem 6 4 min
- Problem 8 3 min
- Problem 2 4 min
- Problem 11 1 min
- Problem 12 4 min
- Problem 13 4 min
- Concept 1 min
- Problem 4 3 min
- Problem 2 8 min
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Radical Expressions and Equations
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Vocabulary of Quadratic Polynomials - Concept
- Explanation
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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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
Start studying Solving Quadratic Equations Vocabulary. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
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...
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.
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
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:
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 .
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.
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
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
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
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 ...
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."
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 ...
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 ...
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 ...