Algebra 2. Lesson 5-3 Graph y = (x + 1) 2 – 2. 2323 Step 1:Graph the vertex (–1, –2). Draw the axis of symmetry x = –1. Step 2:Find another point. When.

Slides:

Advertisements

Similar presentations

Algebra II w/ trig 4.1 Quadratic Functions and Transformations

Advertisements

If the leading coefficient of a quadratic equation is positive, then the graph opens upward. axis of symmetry f(x) = ax2 + bx + c Positive #

Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd The quadratic function.

9-1 Graphing Quadratic Functions

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

Graph an equation of a parabola

+ Translating Parabolas § By the end of today, you should be able to… 1. Use the vertex form of a quadratic function to graph a parabola. 2. Convert.

EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x x – 7. a. Find the axis of symmetry of the graph of the function.

9.2 Key Features of a Parabola

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.

Introduction A system of equations is a set of equations with the same unknowns. A quadratic-linear system is a system of equations in which one equation.

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

Goal: Graph quadratic functions in different forms.

Lesson 9-2 Graphing y = ax + bx + c Objective: To graph equations of the form f(x) = ax + bx + c and interpret these graphs. 2 2.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.7 – Analyzing Graphs of Quadratic.

Holt McDougal Algebra Properties of Quadratic Functions in Standard Form This shows that parabolas are symmetric curves. The axis of symmetry is.

ALGEBRA 2 Write an equation for a graph that is the set of all points in the plane that are equidistant from point F(0, 1) and the line y = –1. You need.

Solving Polynomial Equations in Factored Form Lesson 10.4A Algebra 2.

Do Now: Pass out calculators. Work on Practice EOC Week # 12 Write down your assignments for the week for a scholar dollar.

Graphing Quadratic Equations Standard Form & Vertex Form.

Objectives Vocabulary zero of a function axis of symmetry

5.1 Graphing Quadratic Functions Algebra 2. Learning Check I can graph quadratic equations of the form y = (x – h) 2 + k, and identify the vertex and.

Objective: To us the vertex form of a quadratic equation 5-3 TRANSFORMING PARABOLAS.

Graphing Quadratic Equations

Unit 1B quadratics Day 3. Graphing a Quadratic Function EQ: How do we graph a quadratic function that is in vertex form? M2 Unit 1B: Day 3 Lesson 3.1B.

Give the coordinate of the vertex of each function.

Graphing Quadratic Functions

2.3 Quadratic Functions. A quadratic function is a function of the form:

Sketching a Quadratic Graph Students will use equation to find the axis of symmetry, the coordinates of points at which the curve intersects the x-axis,

Vertex & axis of Symmetry I can calculate vertex and axis of symmetry from an equation.

GRAPHING QUADRATIC FUNCTIONS

7-3 Graphing quadratic functions

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.

Modeling Data With Quadratic Functions

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

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.

Vertex form Form: Just like absolute value graphs, you will translate the parent function h is positive, shift right; h is negative, shift left K is positive,

5.3 Transformations of Parabolas Goal : Write a quadratic in Vertex Form and use graphing transformations to easily graph a parabola.

Mathematical Studies for the IB Diploma © Hodder Education The quadratic function.

Ch. 5 Notes Page 31 P31 5.3: Transforming Parabolas “I am only one, but I am one. I cannot do everything, but I can do something. And I will not let what.

Quadratic Functions Sketching the graph of Quadratic Functions.

WARM UP What is the x-coordinate of the vertex? 1.y = -2x 2 + 8x – 5 2.y = x 2 + 3x -2 4.

9-3 Graphing y = ax + bx + c 2 1a. y = x - 1 for -3

WARM-UP: Graphing Using a Table x y = 3x  2 y -2 y = 3(-2)  2 -8 y = 3(-1)  y = 3(0)  y = 3(1)  y = 3(2)  2 4 GRAPH. y = 3x 

Unit 1B Quadratics Day 2. Graphing a Quadratic Function EQ: How do we graph a quadratic function in standard form? M2 Unit 1B: Day 2 Lesson 3.1A.

Do Now: Solve the equation in the complex number system.

5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.

How does the value of a affect the graphs?

Warm Up for Lesson 3.5 1)Solve: x 2 – 8x – 20 = 0 2) Sketch the graph of the equation y = 2x – 4.

Graphing Quadratic Equations SECTION 1.1. WHAT IS A QUADRATIC EQUATION? An equation of the form: y = ax 2 + bx + c (a, b, and c are constants) When graphed,

Objectives: Be able to graph a quadratic function in vertex form Be able to write a quadratic function in vertex form (2 ways)

Quadratic Functions Sections Quadratic Functions: 8.1 A quadratic function is a function that can be written in standard form: y = ax 2 + bx.

10-2 Graphing Quadratic Functions. Quadratic Functions (y = ax 2 +bx+c) When a is positive, When a is negative, When c is positive When c is negative.

10.3 Solving Quadratic Equations – Solving Quadratic Eq. Goals / “I can…”  Solve quadratic equations by graphing  Solve quadratic equations using.

Standard Form of a Quadratic Function Lesson 4-2 Part 1

Section 5-3 Transforming Parabolas. Standard form vs Vertex Form  Standard form is y = ax 2 +bx+c  Vertex form is y = a(x-h) 2 + k.

Algebra 2 Step 1:Graph the vertex, which is the y-intercept (0, 1). Step 2:Make a table of values to find some points on one side of the axis of symmetry.

Algebra Lesson 10-2: Graph y = ax2 + bx + c

Algebra I Section 9.3 Graph Quadratic Functions

Warm Up circle hyperbola circle

parabola up down vertex Graph Quadratic Equations axis of symmetry

Find the x-coordinate of the vertex

Bellringer Find the equation of the parabola given the following points, then find the axis of symmetry and the minimum value. (-3,-2), (-4,1), (0,1)

Lesson 5.3 Transforming Parabolas

Drawing Graphs The parabola x Example y

Section 10.2 “Graph y = ax² + bx + c”

Presentation transcript:

Algebra 2

Lesson 5-3 Graph y = (x + 1) 2 – Step 1:Graph the vertex (–1, –2). Draw the axis of symmetry x = –1. Step 2:Find another point. When x = 2, y = (2 + 1) 2 – 2 = 4. Graph (2, 4) The graph of y = (x + 1) 2 – 2 is a translation of the graph of the parent function y = x You can graph it by translating the parent function or by finding the vertex and the axis of symmetry. Step 3:Graph the point corresponding to (2, 4). It is three units to the left of the axis of symmetry at (–4, 4). Step 4:Sketch the curve. Transforming Parabolas Additional Examples

Algebra Example 1.Graph the function y = 4(x – 3) 2. 2.Identify the vertex and the y-intercept of the graph of y = –2(x + 5) (–5, 8), –42

Algebra 2 Write the equation of the parabola shown below. Lesson 5-3 y = a(x – h) 2 + kUse the vertex form. y = a(x – 2) 2 – 5Substitute h = 2 and k = –5. –3 = a(0 – 2) 2 – 5Substitute (0, –3). 2 = 4aSimplify. = aSolve for a The equation of the parabola is y = (x – 2) 2 – Transforming Parabolas Additional Examples

Algebra 2 Write y = –7x 2 – 70x – 169 in vertex form. Lesson 5-3 The vertex is at (–5, 6). The vertex form of the function is y = –7(x + 5) y = –7 (–5) 2 – 70(–5) – 169 = 6 Find the y-coordinate of the vertex. = –7(x – (–5)) y = a(x – h) 2 + kWrite in vertex form. Substitute for a, h and k. = –7(x + 5) Transforming Parabolas b 2a x = – = – (–70) 2(–7) = –5 Find the x-coordinate of the vertex. Substitute for a and b. Additional Examples

Algebra Example 3.Write the equation y = 3x x – 1 in vertex form. y = 3(x + 2) 2 – 13