Quadratics Day 2! VERTEX FORM Unit 6 Quadratic Functions Math II.

Slides:

Advertisements

Similar presentations

5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Advertisements

MTH 065 Elementary Algebra II Chapter 11 Quadratic Functions and Equations Section 11.7 More About Graphing Quadratic Functions.

Introduction A theorem is statement that is shown to be true. Some important theorems have names, such as the Pythagorean Theorem, but many theorems do.

Graphing Quadratic Functions

13.2 Solving Quadratic Equations by Graphing CORD Math Mrs. Spitz Spring 2007.

Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

Solve a linear-quadratic system by graphing

Converting Quadratic Equations

Write a quadratic function in vertex form

Warm Up Write each expression as a trinomial. Factor each expression.

Standard 9 Write a quadratic function in vertex form

5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Solving Quadratics by Completing the Square, continued Holt Chapter 5 Section 4.

5.4 – Completing the Square Objectives: Use completing the square to solve a quadratic equation. Use the vertex form of a quadratic function to locate.

Quadratic Functions. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below. If the coefficient.

The General Quadratic Function Students will be able to graph functions defined by the general quadratic equation.

Goal: Graph quadratic functions in different forms.

Warmup 9-11 Solve the following equations by factoring. Show work! 1.x x - 80 = 0 2.Solve by using the quadratic formula: 4x 2 - 5x - 2 = 0 3.Solve.

Factor and Solve: 1.x² - 6x – 27 = 0 2.4x² - 1 = 0 Convert to Vertex Format by Completing the Square (hint: kids at the store) 3. Y = 3x² - 12x + 20.

Objectives Solve quadratic equations by completing the square.

Converting Quadratic Equations A step-by-step guide with practice.

 What are the three forms a quadratic equation can be written in? Vertex Standard Factored.

Algebra-2 Lesson 4-3A (Intercept Form). Quiz 4-1, What is the vertex of: 2. What is the vertex of:

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.

Finding a Quadratic Equation from Three Coordinates.

For a quadratic function, how to find the coordinates of the vertex of its graph? 2. Functions and Graphs (a) For y = a(x - h) 2 +k, the vertex of the.

Objectives Vocabulary zero of a function axis of symmetry

Graphing Quadratic Functions

Quadratics cutting axis (2) Algebra Quadratics cutting the x and y axis. In each of the examples which follow, you are asked to a) Find the points where.

GRAPHING QUADRATIC FUNCTIONS

Lesson 5.2 AIM: Review of Vertex and Axis of Symmetry.

Warm-Up Factor. 6 minutes 1) x x ) x 2 – 22x ) x 2 – 12x - 64 Solve each equation. 4) d 2 – 100 = 0 5) z 2 – 2z + 1 = 0 6) t

Algebra-2 Lesson 4-3B (Solving Intercept Form). Quiz 4-1, What is the vertex of: 2. What is the vertex of:

Graphing Quadratic Equations in Standard Form

Introduction Quadratic functions are used to model various situations. Some situations are literal, such as determining the shape of a parabola, and some.

WARM UP Use f(x) = 3x 2 + 4x – 6 to evaluate the following. 1. f(2) 2. f(-4) 3. f(0)

Graphing quadratic functions part 2. X Y I y = 3x² - 6x + 2 You have to find the vertex before you can graph this function Use the formula -b 2a a = 3.

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

CHANGING FORMS OF QUADRATICS. Converting from Vertex Form to Standard Form  Multiply out the binomial squared.  Distribute if there is a term out front.

Daily Check Give the transformations for each of the following functions? 1)f(x) = (x - 2) )f(x) = -3x 2 3)f(x) = ½ (x+3) 2 Write the equation in.

Concept 24 Essential Question/Topic: I can change a quadratic from standard form into vertex form.

Quiz 4-1, What is the vertex of: 2. What is the vertex of:

2-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

5.4 – Completing the Square

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you can use square roots.

Objectives Solve quadratic equations by completing the square.

Introduction The equation of a quadratic function can be written in several different forms. We have practiced using the standard form of a quadratic function.

Daily Check Give the transformations for each of the following functions? f(x) = (x - 2)2 + 4 f(x) = -3x2 f(x) = ½ (x+3)2 Write the equation in vertex.

Solving Quadratic Equations by the Complete the Square Method

Pick a category a point value

5.5 Completing the Square.

PRESENTED BY AKILI THOMAS, DANA STA. ANA, & MICHAEL BRISCO

Algebra II Exit Pass Lines - Review FLY SWATTER

Quadratics in Vertex Form

Bahm’s EIGHT Steps to Graphing Quadratic Equations (y = ax2 + bx + c) like a CHAMPION! Find the axis of symmetry (x = -b/2a) Substitute.

4.7 Complete the Square.

5.5 Completing the Square.

Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9 3

Review: Simplify.

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

CCGPS Geometry Day 39 (3-5-15)

Obj: graph parabolas in two forms

Section 10.2 “Graph y = ax² + bx + c”

L5-7 Objective: Students will be able to solve quadratics by using the quadratic formula.

Presentation transcript:

Quadratics Day 2! VERTEX FORM Unit 6 Quadratic Functions Math II

VERTEX FORM ! y = a (x – h ) 2 + k -Where a is the same a from Standard Form -The Vertex of the quadratic is at ( h, k ) -We can easily graph a quadratic when it is in vertex form

Converting from Vertex to Standard Form Example: y = -2(x – 4) = -2(x 2 – 8x + 16) + 5 = -2x x – = -2x x – 27 Vertex Form: Square the binomial Distribute the coefficient of the trinomial…. Combine “like” terms Standard Form!

Example: Convert each quadratic to Standard Form. 1.y = 5(x + 2) 2 – 9 1.y = -3(x – 4) (x – 2) 2 + 6

Review Example: Find the Axis of Symmetry of Vertex. 1.y = -2x 2 + 4x – 9 a = ____, b = ____, c = ____ 1.y = x 2 – 10 a = ____, b = ____, c = ____ 1.y = x 2 + 4x – 1 a = ____, b = ____, c = ____ 1.y = -2x 2 + 8x – 8 a = ____, b = ____, c = ____

Converting Standard Form to Vertex Form Step 1 : Determine the a value from standard form Step 2 : Find the vertex. – Use x = -b/2a to find the x coordinate – Substitute x in for the original equation to find y Step 3 : Substitute vertex and a to vertex form.

Example: Convert the quadratic to Vertex Form. a = 8  b = -16, c = 27 Vertex: (x-coordinate) (y-coordinate) Vertex : (1, 19) Vertex Form: y = 8(x – 1) y = 8x 2 – 16x + 27

Example: Convert the quadratic to Vertex Form. y = 5x 2 – 40x + 67

Your turn!: Convert the quadratic to Vertex Form. 1.y = x 2 – 9 1.y = 7x x y = -2x 2 – 24x – 75

Writing the equation of a Quadratic given the vertex and a point.. Example: Find the equation of the quadratic with vertex (0, 0) and passes through the point (-2, 8) y = a (x – 0) Substitute vertex in for h and k 8 = a (-2 – 0) 2 + 0Substitute x and y values in 8 = a (-2) 2 Simplify and solve for a 8 = 4 a 2 = a Vertex Form: y = 2(x – 0) OR y = 2x 2

Example: Find each quadratic function with the given vertex that passes through the given point. Write in Standard Form. 1.Vertex (2, 0) passing through (1, 3) 1.Vertex (-3, 0) passing through (-5, -4) 1.Vertex (2, 5) passing through (3, 7) 1.Vertex (-3, 4) passing through (0, 0)