AIM #1.5: How do we solve quadratic equations?

Slides:

Advertisements

Similar presentations

How do I solve quadratic equations? Notes Over Solving Quadratics Methods of Solving Quadratics Square Root Method: No bx term.

Advertisements

EXAMPLE 1 Solve a quadratic equation by finding square roots Solve x 2 – 8x + 16 = 25. x 2 – 8x + 16 = 25 Write original equation. (x – 4) 2 = 25 Write.

7.1 – Completing the Square

Section 1.5 Quadratic Equations

SOLVING QUADRATIC EQUATIONS COMPLETING THE SQUARE Goal: I can complete the square in a quadratic expression. (A-SSE.3b)

Solving Quadratic Equations by the Quadratic Formula

Quadratic Equations, Functions, and Models

Completing the Square.

Section 1.5 Quadratic Equations. Solving Quadratic Equations by Factoring.

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

Completing the Square 4-6 Day 1 Today’s Objective: I can use the process of completing the square to solve or rewrite a quadratic equation.

Solving Quadratic Equations. Solving by Factoring.

Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.

Lesson 10.5 Factoring Objective: To factor a quadratic trinomial of the form Factoring a trinomial is the opposite of multiplying two binomials. Example:

Section 1.4 – Quadratic Equations

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

8-1 Completing the Square

Martin-Gay, Beginning Algebra, 5ed 22 Not all quadratic equations can be solved as in the previous examples. By using a method called completing the square,

Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.

1.3 Quadratic Equations College Algebra: Equations and Inequalities.

Quadratic Formula. Solve x 2 + 3x – 4 = 0 This quadratic happens to factor: x 2 + 3x – 4 = (x + 4)(x – 1) = 0 This quadratic happens to factor: x 2.

Section 1.4 Day 1 – Quadratic Equations No Calculator After this section you should be able to: Solve quadratic equations by FACTORING.

ANSWERS!. Completing the Square Level 1 Answers Completing the Square Level 2 Answers.

Solve a quadratic equation by finding square roots

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

Warm-Up 1. Find the -Vertex -Y-Intercept -X-intercepts 2. Graph 3. Factor.

Solving Quadratic Equations by the Quadratic Formula

Quadratic Equations P.7.

Objectives Solve quadratic equations by completing the square.

Factor the expression. If the expression cannot be factored, say so.

Solving Quadratic Equations by the Quadratic Formula

8-6 Solving Quadratic Equations using Factoring

Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equations by Completing the Square

3.3: The Quadratic Formula

Solve a quadratic equation

Solving Quadratic Equations by the Quadratic Formula

Section 1.5 Quadratic Equations

Completing the Square CA 14.0, 23.0.

Solving Quadratic Equations by the Quadratic Formula

3.4 Solving Simple Quadratic Equations, Completing the Square, and Solving Equations using Completing the Square.

Warm-Up Factor the following trinomials. What do you notice?

The Square Root Property and Completing the Square

Quadratic Equations and Functions

Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equations

Review: Simplify.

Section 9.5 Day 1 Solving Quadratic Equations by using the Quadratic Formula Algebra 1.

The Square Root Property and Completing the Square

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.

Objective - To solve quadratic equations by completing the square.

Quadratic Equations.

Solving Quadratic Equations by the Quadratic Formula

Warm-Up: September 30 / October 1, 2015 Factor each expression

Solving Quadratic Equations by Factoring

Solving the Quadratic Equation by Completing the Square

Lessons The quadratic Formula and the discriminant

Questions over HW?. Skills Check Radical Operations and Solving by Square Roots after HW Check.

Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equations by the Quadratic Formula

Let’s see why the answers (1) and (2) are the same

Solve quadratic equations using the: QUADRATIC FORMULA

Solve using factoring or square root property.

5.6 Solving Quadratic Equations by the Quadratic Formula

3.4 Solve by Factoring (Part 2)

Bell Ringer (in your Math Journal)

Solving Quadratic Equations by the Quadratic Formula

Presentation transcript:

AIM #1.5: How do we solve quadratic equations?

What is a quadratic Equation?

How do we solve quadratic Equations? Square root Property Factoring Complete the square Quadratic formula Graphing (will visit in 1.5 B)

How do we solve quadratics using the square root property?

Example 1: Solve the quadratics

Check for Understanding: Solve. 3𝑥 2 =27 𝑥+2 2 =25

What is the zero product principle?

How do we solve quadratics by factoring?

Example 2: Solve by factoring.

Check for Understanding: 𝑥 2 −3𝑥 −10=0 𝑥 2 =8𝑥−15 3 𝑥 2 −2𝑥=8

How do we solve by completing the square?

Why do we call it complete the square? Why we call this completing the square.

Example 3: What term should be added to each binomial so that it becomes a perfect square trinomial? Write and factor the trinomial.

Check for Understanding: What term should be added to each binomial so that it becomes a perfect square trinomial? Write and factor the trinomial. 𝒙 𝟐 +𝟏𝟐𝒙 𝒙 𝟐 −𝟏𝟎𝒙

Solve using complete the square Example 4: Solve using complete the square

Check for Understanding: Solve the equation by completing the square. 𝑥 2 +6𝑥=7

How do we solve using the quadratic formula?

Solve using the quadratic formula Example 5: Solve using the quadratic formula

Check For Understanding: Solve using the quadratic formula. 3𝑥 2 −3𝑥−4=0

What is the function of the discriminant?

Example 6: Compute the discriminant and determine the number and type of solutions:

Check for Understanding: Compute the discriminant and determine the number and type of solutions: 𝑥 2 −4𝑥−5=0 2 𝑥 2 −11𝑥+3=0

Summary: Answer in complete sentences. What are the four ways to solve quadratic equations? For each equation below which strategy would recommend then solve. 𝟑 𝒙 𝟐 =𝟔𝟎 𝒙 𝟐 −𝟐𝒙=𝟏 𝒙 𝟐 −𝟔𝒙+𝟏𝟑=𝟎

Solution to summary: