x2 - 4x = 32 The sum of the solutions is:

Slides:



Advertisements
Similar presentations
Solve a System Algebraically
Advertisements

Algebra Recap Solve the following equations (i) 3x + 7 = x (ii) 3x + 1 = 5x – 13 (iii) 3(5x – 2) = 4(3x + 6) (iv) 3(2x + 1) = 2x + 11 (v) 2(x + 2)
Quadratic Equations Sum and Product of the Roots.
Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =
7.1 – Completing the Square
4.8 Quadratic Formula and Discriminant
4.8: Quadratic Formula HW: worksheet
Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula. Discriminant.
Tactic 17: Add Equations. When a question involves two or more equations, try adding the equations together. Many questions involving systems of equations.
Do Now: Factor x2 – 196 4x2 + 38x x2 – 36 (x + 14)(x – 14)
Solving Quadratic Equations by Factoring. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x².
The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)
Essential Question: How do you use the quadratic formula and the discriminant? Students will write a summary including the steps for using the quadratic.
Review of Radicals and Quadratic Equations Lesson 9.1.
Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.
2.6 Solving Quadratic Equations with Complex Roots 11/9/2012.
Twenty Questions Algebra Review Twenty Questions
Whiteboardmaths.com © 2008 All rights reserved
5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.
ALGEBRA 1 SECTION 10.4 Use Square Roots to Solve Quadratic Equations Big Idea: Solve quadratic equations Essential Question: How do you solve a quadratic.
Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.
Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0
Lesson 5-6: Quadratic Formula Algebra II CP Mrs. Mongold.
7-6 USING THE QUADRATIC FORMULA ALGEBRA 1 CP OBJECTIVE: USING THE QUADRATIC FORMULA TO SOLVE QUADRATIC EQUATIONS.
Solving a Trigonometric Equation Find the general solution of the equation.
Notes Over 5.6 Quadratic Formula
4.8 “The Quadratic Formula” Steps: 1.Get the equation in the correct form. 2.Identify a, b, & c. 3.Plug numbers into the formula. 4.Solve, then simplify.
Quadratic and Rational Inequalities
Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.
Table of Contents Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula.
x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.
Title: ch. 6 Algebra: quadratic equations. Learning Objective: WALT solve quadratic equations by using the quadratic formula. p.143.
MATH II – QUADRATICS to solve quadratic equations. MATH III – MATH II –
EXAMPLE 1 Solve an equation with two real solutions Solve x 2 + 3x = 2. x 2 + 3x = 2 Write original equation. x 2 + 3x – 2 = 0 Write in standard form.
3.2 Solve Linear Systems Algebraically Algebra II.
AS Mathematics Algebra – Quadratic equations. Objectives Be confident in the use of brackets Be able to factorise quadratic expressions Be able to solve.
Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions.
Do Now Determine which numbers in the set are natural, whole, integers, rational and irrational -9, -7/2, 5, 2/3, √2, 0, 1, -4, 2, -11 Evaluate |x + 2|,
Notes P.5 – Solving Equations. I. Graphically: Ex.- Solve graphically, using two different methods. Solution – See graphing Calculator Overhead.
Solve equations by factoring.
The Quadratic Formula..
Solving Quadratic Equations by the Complete the Square Method
Ms. Pain, the algebra teacher, has a habit of standing in front of crucial information . If she did the problem correctly (and she always does!), what.
8.6 Solving Rational Equations
EQUATIONS & INEQUALITIES
Solve Quadratic Equations by the Quadratic Formula
If a point has coordinates (x,y) and xy < 0 and y > 0 the point
Quadratic Equations.
Solve an equation with two real solutions
Sullivan Algebra and Trigonometry: Section 1.3
Solving Equations by Factoring and Problem Solving
4.8 Use the Quadratic Formula & the Discriminant
Class Notes 11.2 The Quadratic Formula.
The Quadratic Formula.
10.7 Solving Quadratic Equations by Completing the Square
10.4 Solving Equations in Factored Form
Objective Solve equations in one variable that contain variable terms on both sides.
Solving Quadratics by Factoring
Equations and Inequalities
Objective Solve equations in one variable that contain variable terms on both sides.
Solving Equations 3x+7 –7 13 –7 =.
Which of the following rational expressions is defined for x = 3 but undefined for x = -2? F.) None of these.
Solving Quadratic Equations by Factoring
Lesson 7.3 Using the Quadratic Formula
9-5 Factoring to Solve Quadratic Equations
The Quadratic Formula..
The Quadratic Formula..
Algebra 1 Warm Ups 12/11.
Presentation transcript:

x2 - 4x = 32 The sum of the solutions is: Use factoring to solve the quadratic equation. x2 - 4x = 32 The sum of the solutions is: A.) 12 B.) 4 C.) -12 D.) -4 E.) 0 F.) None of these

The sum of the solutions is: Solve by factoring: (x+2)(x-1) = 4 The sum of the solutions is: A.) 1 B.) -5 C.) -2 D.) 5 E.) -1 F.) None of these

The sum of the solutions is: Solve by factoring: (2x-3) (x-4) = (x-5)(x+3) + 7 The sum of the solutions is: A.) 1 B.) 9 C.) -2 D.) -9 E.) -1 F.) None of these

D.) x + 1 E.) -x - 2 F.) None of these Ms. Pain, the algebra teacher, has a habit of standing in front of crucial information . If she did the problem correctly (and she always does!), what is she blocking? Solve: 2 3 -1 2 6x2 x = = 0 x = A.) -x - 1 B.) 2x - 3 C.) 3x - 2 D.) x + 1 E.) -x - 2 F.) None of these

A.) I and II B.) II and III C.) I and III Two of these quadratic equations share a common solution (i.e. one number is a solution to both equations). Find the two equations. I.) x2 = 24 - 5x II.) 2x2 + 2x = 24 III.) x2+ 32 = 12x Ice Cream is always a solution! A.) I and II B.) II and III C.) I and III

A.) I and II B.) II and III C.) I and III Two of these quadratic equations share a common solution (i.e. one number is a solution to both equations). Find the two equations. I.) 2x2 - 3x = 35 II.) 3x2+ 11x - 20 = 0 III.) 6x2 +29x = - 28 A.) I and II B.) II and III C.) I and III

Solve for x: x2 = C.) x = B.) x = A.) x = - D.) x = F.) None of these E.) x =

Solve for x: x2 - = ( ) B.) x = - C.) x = D.) x = F.) None of these + ( ) + A.) x = B.) x = - C.) x = + D.) x = + + E.) x = F.) None of these

(x- )2 = x = 1 x = 4 A.) 3/2 B.) 9/2 C.) 3/4 D.) 9/4 E.) 7/2 Ms. Pain, the algebra teacher, has a habit of standing in front of crucial information . If she did the problem correctly (and she always does!), what number is she blocking? (x- )2 = 5 2 x = 1 x = 4 A.) 3/2 B.) 9/2 C.) 3/4 D.) 9/4 E.) 7/2 F.) None of these

2x2 - x - 4 = 0 Which number is one of the solutions to the equation? D.) C.) E.) None of these

Which number is one of the solutions to the equation? 3x2 - 5x - 1 = 0

Which number is one of the solutions to the equation? 2x2 - 4x - 1 = 0

Which number is one of the solutions to the equation? 7x2 - 8x + 2 = 0

a = 2 b= -3 c = -5 While solving a quadratic equation using the quadratic formula, a study group spilled coffee on their paper. Which of the equations below could have been the original equation? A.) 2(x2 - x) = x + 5 B.) (2x+5)(x - 1) = 0 C.) 2x2 - 1 = 3x - 4 D.) 2x2 - 5x + 2 = 7 - 2x E.) 3x - 5 = -2x2 F.) None of these

Which statements are True?? I.) If x2 = p and p ≥ 0, then x = II.) If AB = 0, then A = 0 or B = 0 or both are = 0 III.) If AB > 0, then either A > 0 and B > 0 or both > 0 A.) I B.) II C.) III D.) 1, II E.) I, III F.) II, III