EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x 2 + 12x – 7. a. Find the axis of symmetry of the graph of the function.

Slides:

Advertisements

Similar presentations

Do Now 4/13/10 Take out homework from yesterday.

Advertisements

Algebra II w/ trig 4.1 Quadratic Functions and Transformations

EXAMPLE 1 Graph y= ax 2 where a > 1 STEP 1 Make a table of values for y = 3x 2 x– 2– 1012 y12303 Plot the points from the table. STEP 2.

QUADTRATIC RELATIONS Standard Form.

EXAMPLE 1 Graph a function of the form y = ax 2 Graph y = 2x 2. Compare the graph with the graph of y = x 2. SOLUTION STEP 1 Make a table of values for.

4.2: Graphs of Quadratic Functions in Vertex or Intercept Form

EXAMPLE 3 Graph a quadratic function in intercept form

Adapted from Walch Education  The standard form of a quadratic function is f ( x ) = ax 2 + bx + c, where a is the coefficient of the quadratic term,

Use intercepts to graph an equation

EXAMPLE 3 Write an equation for a function

EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form x = – Write original equation Graph x = – y.

Graph an equation of a parabola

5.1 Quadratic Function 11/30/12. Graph is a parabola Vocabulary Quadratic Function : a function that is written in the standard form: y = ax 2 + bx +

Write a quadratic function in vertex form

Standard 9 Write a quadratic function in vertex form

2.11 Warm Up Graph the functions & compare to the parent function, y = x². Find the vertex, axis of symmetry, domain & range. 1. y = x² y = 2x².

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

Goal: Graph quadratic functions in different forms.

EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given.

3. Graph Quadratic Functions in Standard Form 3.1 Graph Quadratic Functions in Standard Form WEDNESDAY JAN 26 TH p. 56.

Warm-Up Exercises Find the x -intercept and y -intercept x3x 5y5y = – 5 ; 3 – ANSWER y 2x2x = ANSWER ; 7 – 2 7.

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

9.3 Graphing Quadratic Functions

Graphing Quadratic Equations

Warm Up #2 Find the Product: a. (x – 5)2 b. 4(x +5)(x – 5) ANSWER

WARM UP Simplify (-14) x 2, for x = 3 4.

Unit 1: Function Families Lesson 5: Transformations & Symmetry Notes Graph y = ax 2 + bx + c.

Chapter 9.1 Notes. Quadratic Function – An equation of the form ax 2 + bx + c, where a is not equal to 0. Parabola – The graph of a quadratic function.

10-2 Quadratic Functions Graphing y = ax² + bx + c Step 1 Find the equation of the axis of symmetry and the coordinates of the vertex. Step 2 Find.

EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c Graph y = 2x 2 – 8x + 6. SOLUTION Identify the coefficients of the function. The coefficients.

QUADRATIC FUNCTIONS IN STANDARD FORM 4.1B. Review  A quadratic function can be written in the form y = ax 2 + bx + c.  The graph is a smooth curve called.

REVIEW FOR QUIZ 3 ALGEBRA II. QUESTION 1 FACTOR THE FOLLOWING QUADRATIC 3N 2 + 7N + 4 Answer: (3n + 4)(n + 1)

10.2 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Graph y = ax 2 + bx + c.

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

Warm Up Lesson 4.1 Find the x-intercept and y-intercept

Lesson 9.2: Graph Essential Question: How do you graph general quadratic functions? Common Core CC.9-12.F.BF.3 Graph linear and quadratic functions and.

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 

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

Key Words quadratic function parabola vertex axis of symmetry monomial binomial.

Graphing Quadratics in Vertex and Intercept Form Vertex Form y = a(x – h) 2 + k Intercept Form y = a(x – p)(x – q)

Chapter 4 Section 1. (highest power of x is 2) EXAMPLE 1 Graph a function of the form y = ax 2 Graph y = 2x 2. Compare the graph with the graph of y.

Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y = 3x 2. ANSWER x = 0 2. Identify the vertex of the graph of y = 3x 2. ANSWER (0,

Write a quadratic function in vertex form

How To Graph Quadratic Equations Standard Form.

Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2

5-2 Properties of Parabolas

How to Graph Quadratic Equations

How To Graph Quadratic Equations

parabola up down vertex Graph Quadratic Equations axis of symmetry

Quadratic Functions.

3.1 Quadratic Functions and Models

Before: March 15, 2018 Tell whether the graph of each quadratic function opens upward or downward. Explain. y = 7x² - 4x x – 3x² + y = 5 y = -2/3x².

Find the x-coordinate of the vertex

8.4 - Graphing f (x) = a(x − h)2 + k

How To Graph Quadratic Equations.

Review: Simplify.

Objectives Find the zeros of a quadratic function from its graph.

Objective Graph a quadratic function in the form y = ax2 + bx + c.

3.1 Quadratic Functions and Models

Drawing Graphs The parabola x Example y

How To Graph Quadratic Equations.

Graphing Quadratics of ax2 +bx + c

Section 10.2 “Graph y = ax² + bx + c”

Find the x-intercept and y-intercept

Functions and Their Graphs

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

Honors Algebra 2 Chapter 4

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

How To Graph Quadratic Equations.

Presentation transcript:

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. b. Find the vertex of the graph of the function.

EXAMPLE 1 Find the axis of symmetry and the vertex SOLUTION 12 2(– 2) x = –x = – b 2a = = 3= 3 Substitute – 2 for a and 12 for b. Then simplify. For the function y = –2x x – 7, a =  2 and b = 12. a. b. The x- coordinate of the vertex is, or 3. b 2a – y = –2(3) (3) – 7 = 11 Substitute 3 for x. Then simplify. ANSWER The vertex is (3, 11).

EXAMPLE 2 Graph y = ax 2 + bx + c Graph y = 3x 2 – 6x + 2. Determine whether the parabola opens up or down. Because a > 0, the parabola opens up. STEP 1 STEP 2 = Find and draw the axis of symmetry: x = – b 2a2a – – 6– 6 2(3) =1. STEP 3 Find and plot the vertex.

EXAMPLE 2 To find the y- coordinate, substitute 1 for x in the function and simplify. y = 3(1) 2 – 6(1) + 2 = – 1 So, the vertex is (1, – 1). STEP 4 Plot two points. Choose two x- values less than the x- coordinate of the vertex. Then find the corresponding y- values. Graph y = ax 2 + b x + c The x- coordinate of the vertex is b 2a2a, or 1. –

EXAMPLE 2 Standardized Test Practice x 0 – 1 y 211 STEP 5 Reflect the points plotted in Step 4 in the axis of symmetry. STEP 6 Draw a parabola through the plotted points.

EXAMPLE 2 Graph y = ax 2 + b x + c

GUIDED PRACTICE for Examples 1 and 2 1. Find the axis of symmetry and vertex of the graph of the function y = x 2 – 2x – 3. ANSWER x = 1, (1, –4). 2. Graph the function y = 3x x – 1. Label the vertex and axis of symmetry. ANSWER