Using Square Roots to Solve Quadratic Equations

Jun 29, 2025

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Learn how to solve quadratic equations algebraically using square roots and graphical methods. Improve your math skills and enhance your problem-solving abilities with step-by-step guidance.

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Using Square Roots to Solve Quadratic Equations

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Using Square Roots to Solve Quadratic Equations
Algebraically Solve for x algebraically.
Graphically Solve for x graphically.
Solve for x algebraically.
Solve for x algebraically.

Solving Quadratic Equations by Finding Square Roots

Solving Quadratic Equations by Finding Square Roots. This lesson comes from chapter 9.1 from your textbook, page 503. What is a square root?. If a number square ( b 2 ) = another number ( a ), then b is the square root of a. Example: If 3 2 = 9, then 3 is the square root of 9.

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Solving Quadratic Equations by Finding Square Roots

Solving Quadratic Equations by Finding Square Roots. Inverse Operations…. The opposite of + is - The opposite of is The opposite of x 2 is. Square Root of a Number:. If b 2 = a, then b = (b is a square root of a). Radical Symbol :.

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Solving Quadratic Equations by Using Square Roots

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Roots of quadratic equations

Investigating roots. Solve each of the following quadratic equationsa)x2 7x 12 = 0b)x2 5x 6 = 0 c)x2 x 20 = 0 d)2x2 5x 3 = 0 Write down the sum of the roots and the product of the roots.Roots of polynomial equations are usually denoted by Greek letters.For a quadratic

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Objective: Solve quadratic equations.

Objective: Solve quadratic equations. Warm up Don’t copy problem

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10.4 NOTES Use Square Roots to Solve Quadratic Equations

10.4 NOTES Use Square Roots to Solve Quadratic Equations. Example 1 – Solve Quadratic Equations. Solve the equation. a. c 2 – 25 = 0 b. 2x 2 + 11 = 11. Example 1 Cont. Solve Quadratic Equations. Solve the equation. c. 5w 2 + 12 = -8 d. 25m 2 = 16 .

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ECA Review #20 Quadratic Equations: Square Roots and Factoring

ECA Review #20 Quadratic Equations: Square Roots and Factoring. 20 % of the test will deal with Adding, Subtracting, Multiplying and Factoring Polynomials. Solve the equation for x:. x = 7 x = 5 x = 7 & x = -5 x = 7 & x = 5. [Default] [MC Any] [MC All].

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5.3 Solving Quadratic Equations by Finding Square Roots

5.3 Solving Quadratic Equations by Finding Square Roots. (p. 264) By: L. Keali’i Alicea. How would you solve the equation: x 2 = 4 (take the square root of each side!). * Remember, the square root of a positive # has 2 answers! (one + and one -). Radical. Radical sign. Radicand.

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5.3 Solving Quadratic Equations by Finding Square Roots

5.3 Solving Quadratic Equations by Finding Square Roots. (p. 264). How would you solve the equation: x 2 = 4 (take the square root of each side!). * Remember, the square root of a positive # has 2 answers! (one + and one -). Radical. Radical sign. Radicand. Properties of Square Roots.

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9.6 Solving Quadratic Equations by Using Square Roots

9.6 Solving Quadratic Equations by Using Square Roots. Warm Up Find each square root. Solve each equation. 5 . – 6 x = – 60 6. 7. 2 x – 40 = 0 8. 5 x = 3. 1. 6. 11. 2. 4. –25. 3. x = 80. x = 10. x = 20. California Standards.

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5-3 Solving Quadratic Equations by finding Square Roots.

5-3 Solving Quadratic Equations by finding Square Roots. Objective: Solve quadratic functions by finding square roots. Properties of Square Roots (a > 0, b > 0). Product Property :. Quotient Property:. A square root expression is considered simplified IF:. No radicand has a perfect square

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Chapter 4.5 Solve Quadratic Equations by Finding Square Roots

Chapter 4.5 Solve Quadratic Equations by Finding Square Roots. = 4. =. a. =. =. b. = 3. 7. 5. 9. 4. 6. 5. 7. 7 . 4. 2 9. 4. 16. 80. 14. 81. 14. 16. 21. =. c. 81. 16. =. 126. =. d. =. EXAMPLE 1. Use properties of square roots. Simplify the expression.

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Solve quadratic equations by completing the square. Write quadratic equations in vertex form.

Objectives. Solve quadratic equations by completing the square. Write quadratic equations in vertex form. Vocabulary. completing the square.

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10.2 Solving Equations by Using Square Roots

10.2 Solving Equations by Using Square Roots. Objectives: Solve equations of the form ax 2 = k. Solve equations of the form ax 2 = k where x is replaced by an algebraic expression. Standard Addressed: 2.8.11.N. Solve quadratic equations.

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Objective - To solve quadratic equations using the quadratic formula.

Objective - To solve quadratic equations using the quadratic formula. Quadratic Formula. Quadratic Equation. Vertical Motion. Object Dropped. Object Thrown Upward. How long will a ball thrown upwards at 20 ft/sec stay in the air if it is thrown from a 100 ft. cliff?.

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Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant.

Objectives. Solve quadratic equations using the Quadratic Formula. Classify roots using the discriminant. Vocabulary. discriminant. You can use the Quadratic Formula to solve any quadratic equation that is written in standard form, including equations with real solutions or complex solutions.

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Use Square Roots to Solve Quadratic Equations (4.5 and 6)

Use Square Roots to Solve Quadratic Equations (4.5 and 6). December 2 nd. Use Square Roots to Solve Quadratics. Goal: get x 2 alone on one side of the equation. Then you’ll be able square root each side to find x.

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1.5 Solving Quadratic Equations by Finding Square Roots

1.5 Solving Quadratic Equations by Finding Square Roots. (p. 32) How do you simplify radicals? What are the steps to rationalize a denominator? What is a conjugate? How many answers will you get when you solve a quadratic equation by finding square roots?

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5.3 Solving Quadratic Equations by Finding the Square Roots

P ROPERTIES O F S QUARE R OOTS:. ab = a · b a a. √. √. √. b. b. √. √. √. √. √. √. √. √. √. √. Extra Example 1 500 b) 25 c) 2. √. 36. 11. 100 · 5. 25. 5. √.

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To solve quadratic equations by using square roots

To solve quadratic equations by using square roots To solve quadratic equations by using factoring techniques To solve quadratic equations by completing the square To solve quadratic equations by using the Quadratic Formula. To solve quadratic equations by using square roots.

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