Algebra 2: Unit 3 - Vertex Form

Slides:



Advertisements
Similar presentations
1.4 – Shifting, Reflecting, and Stretching Graphs
Advertisements

The vertex of the parabola is at (h, k).
In Chapters 2 and 3, you studied linear functions of the form f(x) = mx + b. A quadratic function is a function that can be written in the form of f(x)
Transform quadratic functions.
2.2 b Writing equations in vertex form
Holt Algebra Using Transformations to Graph Quadratic Functions Transform quadratic functions. Describe the effects of changes in the coefficients.
Objective: To us the vertex form of a quadratic equation 5-3 TRANSFORMING PARABOLAS.
Consider the function: f(x) = 2|x – 2| Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.
Vertex Form of a Parabola
Summary of 2.1 y = -x2 graph of y = x2 is reflected in the x- axis
TRANSFORMATION OF FUNCTIONS FUNCTIONS. REMEMBER Identify the functions of the graphs below: f(x) = x f(x) = x 2 f(x) = |x|f(x) = Quadratic Absolute Value.
UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH
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
Holt McDougal Algebra Using Transformations to Graph Quadratic Functions Warm Up For each translation of the point (–2, 5), give the coordinates.
Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola.
5.3 Transformations of Parabolas Goal : Write a quadratic in Vertex Form and use graphing transformations to easily graph a parabola.
4.1 – 4.3 Review. Sketch a graph of the quadratic. y = -(x + 3) Find: Vertex (-3, 5) Axis of symmetry x = -3 y - intercept (0, -4) x - intercepts.
Parabola Formulas Summary of Day One Findings Horizonal Parabolas (Type 2: Right and Left) Vertical Parabolas (Type 1: Up and Down) Vertex Form Vertex:
Objectives Transform quadratic functions.
 I will be able to identify and graph quadratic functions. Algebra 2 Foundations, pg 204.
Shifting, Reflecting, & Stretching Graphs 1.4. Six Most Commonly Used Functions in Algebra Constant f(x) = c Identity f(x) = x Absolute Value f(x) = |x|
Quadratic Functions and Transformations Lesson 4-1
Warm Up For each translation of the point (–2, 5), give the coordinates of the translated point units down 2. 3 units right For each function, evaluate.
Do-Now What is the general form of an absolute value function?
Lesson 2-6 Families of Functions.
2.6 Families of Functions Learning goals
3.3 Quadratic Functions Quadratic Function: 2nd degree polynomial
Quadratic Equations Chapter 5.
13 Algebra 1 NOTES Unit 13.
Pre-AP Algebra 2 Goal(s):
Using Transformations to Graph Quadratic Functions 5-1
Transformation of Functions
Interesting Fact of the Day
Warm-Up 1. On approximately what interval is the function is decreasing. Are there any zeros? If so where? Write the equation of the line through.
Unit 5 – Quadratics Review Problems
Use Absolute Value Functions and Transformations
2.6 Translations and Families of Functions
Jeopardy!.
Graphs of Quadratic Functions
Transformations: Review Transformations
Objectives Transform quadratic functions.
Translating Parabolas
2.5 Stretching, Shrinking, and Reflecting Graphs
Objectives Transform quadratic functions.
parabola up down vertex Graph Quadratic Equations axis of symmetry
Algebra 1 Section 12.8.
Lesson 5.3 Transforming Parabolas
Chapter 15 Review Quadratic Functions.
Rev Graph Review Parent Functions that we Graph Linear:
TRANSFORMATIONS OF FUNCTIONS
Graph Square Root and Cube Root Functions
Find the x-coordinate of the vertex
Chapter 15 Review Quadratic Functions.
Transformation of Functions
Warm-up: Welcome Ticket
Quadratic Functions and Their Graph
2.7 Graphing Absolute Value Functions
12.4 Quadratic Functions Goal: Graph Quadratic functions
TRANSFORMATIONS OF FUNCTIONS
ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 4-1 and 4-2 (Quadratic Functions and Transformations AND Standard and Vertex Forms) ALGEBRA.
5.3 Graphing Radical Functions
2.7 Graphing Absolute Value Functions
2.1 Transformations of Quadratic Functions
Horizontal Shift left 4 units Vertical Shift down 2 units
Graphing Quadratic Functions in Vertex form
The vertex of the parabola is at (h, k).
4.1 Notes – Graph Quadratic Functions in Standard Form
Jigsaw Review: 4.1 to 4.3 Friday, Nov. 20, 2009
Bell Work Draw a smile Draw a frown Draw something symmetrical.
The graph below is a transformation of which parent function?
Presentation transcript:

Algebra 2: Unit 3 - Vertex Form UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH f(x) Original (Parent) Graph a•f(x – h) + k Transformed Graph “a” – value Stretch or Shrink Graph and Flips for negative “h” – value Shifts the Graph Right or Left “k” – value Shifts the Graph Up or Down For quadratic graphs #1 - 6: y = a(x – h)2 + k TRANSFORMED QUADRATIC FUNCTION y = x2 QUADRATIC FUNCTION (ORIGINAL)

FIND THE EQUATION of the Quadratics in Graphs #1 - 6 Step #1: Use the vertex to indicate the horizontal (h) and vertical (k) changes Step #2: Use another point on the graph to help determine the “a”- value (Hint: The direction it opens indicates the sign) Graph #1: y = a(x – h)2 + k Graph #2: y = a(x – h)2 + k

Graph #3: y = a(x – h)2 + k Graph #4: y = a(x – h)2 + k

Graph #5: y = a(x – h)2 + k Graph #6: y = a(x – h)2 + k

a (+ up; – down) a (+ right; –left) Vertex Form Vertex Form Vertex: QUADRATIC FUNCTIONS – VERTEX FORM SUMMARY Vertical Parabolas (Type 1: Up and Down) Horizontal Parabolas (Type 2: Right and Left) Vertex Form Vertex Form Vertex: Vertex: (h, k) (h, k) Axis: x = h Axis: y = k Rate: a (+ up; – down) Rate: a (+ right; –left)

Find VERTEX FORM EQUATION: Given Vertex & Point Plug vertex (h, k) into appropriate vertex form equation and use another point (x, y) to solve for “a”. [A] Opening Vertical Vertex: (2, 4) Point: (-6, 8) [B] Opening: Horizontal Vertex: (- 4, 6) Point: (2, 8)

Vertex Form to Standard Form of Quadratic Functions FOIL the squared statement. Distribute a-value Combine Like Terms [B] [A]

[D] [C]

Algebra 2: Unit 3 - Vertex Form Standard Form to Vertex Form of Quadratic Functions Vertical Parabolas ( y = ) Graph the Equation in [Y =] Find Vertex using MIN or MAX command in [CALC] a – value is the same in standard and vertex form. [B] [A] a - value: a - value: Vertex: Vertex: Equation: Equation:

Horizontal Parabolas ( x = ) Vertical Parabolas ( y = ): Continued [D] [C] a - value: a - value: Vertex: Vertex: Equation: Equation: Horizontal Parabolas ( x = ) Switch the variables and Graph the Equation in [Y =] Opens Up = Opens Right Opens Down = Opens Left Find Vertex using MIN or MAX command in [CALC] Switch the Min or Max Ordered Pair for actual vertex a – value is the same in standard and vertex form.

Horizontal Parabolas Practice a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation: Equation:

a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation: [D] [C] a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation: Equation: