5-38. Graph. Warm Up a. y = x2 + 6x + 8 0 = x2 + 6x + 8 0 = (x + 2)(x + 4) x + 2 = 0 or x + 4 = 0 x = -2 x = -4 (-2,0) (-4,0) -2 + -4 = -3 2 y = (-3)2.

Slides:

Advertisements

Similar presentations

Factoring a Polynomial. Example 1: Factoring a Polynomial Completely factor x 3 + 2x 2 – 11x – 12 Use the graph or table to find at least one real root.

Advertisements

Solving Quadratic Equations by Graphing 9-5

Finding the Roots of a Polynomial. 2 Real Roots and 2 Complex Roots because it only has 2 x-intercepts but has 4 “turns” Classifying the Roots of a Polynomial.

This is a setup file for a Jeopardy game. Rather than running this presentation, you need to save this PowerPoint file on your computer and then modify.

Section 1.5 Quadratic Equations

10-3: Solving Quadratic Equations

2-3 solving quadratic equations by graphing and factoring

1. Graph the inequality y < 2x + 1.

Solving Quadratic Equations by Graphing 9-5

Topic 5 Solving Quadratic Equations by Graphing Unit 7 Topic 5.

Characteristics of Quadratic Functions Section 2.2 beginning on page 56.

JEOPARDY! Graphing Quadratics Graphing Solving using Square Roots Discriminants GO TO FINAL.

Warm Up 1) Use the graph to Identify the following: a)Vertex: b) Zeros: c) Range: d)Domain: e) Line of symmetry: f)Minimum/Maximum: (-2,-1) -3 and -1 R:

9.4 factoring to solve quadratic equations.. What are the roots of a quadratic function? Roots (x-intercepts): x values when y = 0 ( ___, 0) How do you.

Solving Quadratic Equations

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.

Graphing Quadratic Equations Standard Form & Vertex Form.

5.6: The Quadratic Formula and the Discriminant Objectives: Students will be able to… Solve a quadratic equation using the quadratic formula Use the discriminant.

1) What does x have to be for 3x = 0? 1) What does x have to be for 3(x -2) = 0 2) What does x have to be for (x–2) (x+3) = 0.

Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros.

For each rule make a table, graph, and draw figure 0, 1, and 2.

3.3 Solve Quadratic Equations by Graphing & by Factoring

SWBAT…analyze the characteristics of the graphs of quadratic functions Wed, 2/15 Agenda 1. WU (10 min) 2. Characteristics of quadratic equations (35 min)

The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?

To add fractions, you need a common denominator. Remember!

Polynomials, Factors and Zeros

Holt Algebra Solving Quadratic Equations by Graphing and Factoring Solve quadratic equations by factoring. Find roots of quadratic equations. Graph.

Roots, Zeroes, and Solutions For Quadratics Day 2.

5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.

5.3 Again! Warm-up (IN) Learning Objective: To use factoring to solve quadratic equations. Factor:

SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.

Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.

Table of Contents First get all nonzero terms on one side. Quadratic Equation: Solving by factoring Example: Solve 6x 2 – 13x = 8. 6x 2 – 13x – 8 = 0 Second.

Graphs of Quadratics Let’s start by graphing the parent quadratic function y = x 2.

XY A.O.S.: Vertex: Max. or Min.? X – Intercepts Y – Intercepts.

Lesson 10-2 Solving Quadratic Equations by Graphing.

Solving Quadratic Equations by Factoring. Zero-Product Property If ab=0, then either a=0, b=0 or both=0 States that if the product of two factors is zero.

Two Step Equations with Decimals SWBAT solve two step algebraic equations containing decimals by applying the appropriate properties of equality.

Solving Quadratic Equations Using the Zero Product Property March 18, 2014.

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.

Sample Problems for Class Review

Graphing Quadratic Equations a step-by-step guide with practice.

Characteristics of Quadratic Functions Section 2.2 beginning on page 56.

SWBAT… analyze the characteristics of the graphs of quadratic functions Wed, 6/3 Agenda 1. WU (5 min) 2. Notes on graphing quadratics & properties of quadratics.

Warm Up: Not every U-shaped curve is a parabola or part of a parabola. For instance, a semi-circle seems like part of a parabola. Due to the laws of physics,

PREVIOUSLY YOU LEARNED THAT THE QUADRATIC FORMULA CAN SOLVE ANY QUADRATIC EQUATION AX 2 + BX + C = 0 IF A ≠ 0. BUT WHAT IF THE EQUATION IS NOT IN.

5-49. Several parabolas and equations are shown below. Match each graph with its equation. Justify your choices and share any shortcuts you discover with.

Graphs of Equations Objectives:  Be able to find solutions, intercepts and the symmetry of a graph by hand and by using the calculator. TS: Analyzing.

5-71. Solve the two equations below. Be ready to share your method(s) with the class. a. x 2 + 4x + 1 = 0b. (x + 2) 2 = 3.

Warm Up In previous courses, you have investigated linear and exponential functions. In this chapter, you will study quadratic functions. You will learn.

5-26. WHAT DO YOU NEED TO SKETCH A PARABOLA?  How many points do you need in order to sketch a parabola? One? Ten? Fifty? Think about this as you answer.

A factored form of x 2 + 5x - 24 is — A (x − 4)(x + 6) B (x − 3)(x + 8) C (x − 2)(x + 12) D (x − 6)(x + 4) Which of the following equals when factored.

Quadratic Equations: Solve by factoring Today’s Objective: I can solve quadratic equations.

Solving Quadratic Equations by Graphing  Quadratic Equation- A quadratic function set equal to a value, in the form ax 2 +bx+c, where a≠0  Standard.

SWBAT… solve quadratic equations Mon, 5/23

PIECEWISE FUNCTIONS.

Solving Quadratic equations by graphing.

Solving Quadratics by Factoring

Match graph and equation Not all equations will have a graph

Quadratics – Absolute value

Creating & Graphing Quadratic Functions Using the X-Intercepts (3.3.2)

Objective Solve quadratic equations by factoring..

Solving Quadratic Equations by Factoring

Bellwork: 2/13/18 Find each product.

Have out: U1D6 Bellwork: a) x2 + 10x + 24 b) x3 – 4x2 – 45x

Algebra 1 Warm Ups Nov. 30th.

5-49. Several parabolas and equations are shown below

5-26. WHAT DO YOU NEED TO SKETCH A PARABOLA?

Do Now 3/20/19 Take out HW from last night.

Warmup Graph the following quadratic equation using the table provided. Then analyze the graph for the information listed below. y = -3x2 + 12x.

Presentation transcript:

5-38. Graph. Warm Up a. y = x2 + 6x + 8 0 = x2 + 6x + 8 0 = (x + 2)(x + 4) x + 2 = 0 or x + 4 = 0 x = -2 x = -4 (-2,0) (-4,0) -2 + -4 = -3 2 y = (-3)2 + 6(-3) + 8 y = -1 (-3,-1) b. y = x2 + 6x 0 = x2 + 6x 0 = x(x + 6) x = 0 or x + 6 = 0 x = -6 (0,0) (-6,0) 0 + -6 = -3 2 y = (-3)2 + 6(-3) y = -9 (-3,-9)

5.1.4 Writing Equations for Quadratic Functions HW: 5-43 through 5-48 5.1.4 Writing Equations for Quadratic Functions January 20, 2016

Objectives CO: SWBAT write a quadratic equation from a table by using the Zero Product Property in reverse. LO: SWBAT explain how to use a table to create quadratic equations.

b = partners, rally table 5-39. TABLE TO EQUATION You know how to make a table for a quadratic function, but how can you write an equation when given the table? Write an equation for each table below. What clues in the tables helped you determine the equations? Verify your equations. b. a. x = -3 x + 3 = 0 x = 2 x – 2 = 0 (x + 3)(x – 2) = 0 y = x2 + x - 6 x = -5 x + 5 = 0 x = 1 x – 1 = 0 (x + 5)(x – 1) = 0 y = x2 + 4x - 5 a = together b = partners, rally table

5-40. Gwen is stuck while trying to write the equation for the quadratic function given in the following table. Her teammate Sadie says “This looks like part (a) of the problem we just did, except the y-values are all doubled! How can that help us?” Use Sadie’s observation to help you write the equation of the quadratic function given in the table below. y = 2(x2 + x - 6) y = 2x2 + 2x - 12 TEAM

5-41. WATER BALLOON CONTEST REVISITED Remember Imp’s water balloon launch? Since the water balloon landed on the computer, you were given only a table of data, shown again below. Write an equation that represents the height of Imp’s balloon as it traveled through the air. x = 2 x – 2 = 0 (12,0) must be the other x-intercept by symmetry x = 12 x – 12 = 0 (x – 2)(x – 12) = 0 y = x2 – 14x + 24 y = (3)2 – 14(3) + 24 y = -9 y = -(x2 – 14x + 24) y = -x2 + 14x – 24 Together