4.2A Graph Quadratic Functions in Vertex or Intercept Form Algebra II Algebra II.

Slides:

Advertisements

Similar presentations

An equation for which the graph is a line Any ordered pair of numbers that makes a linear equation true. (9,0) IS ONE SOLUTION FOR Y = X - 9.

Advertisements

4.1: Do Now Time (hours)02357 Height (millimeters) John placed a container outside during a rainstorm. A gauge on the side of the container shows.

1.2 Graphing Quadratic Functions In Vertex or Intercept Form

Intercept, Standard, and Vertex Form

Daily Check 1.Factor: 3x x Factor and Solve: 2x 2 - 7x + 3 = 0.

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.

5.1 Graphing Quadratic Functions (p. 249) Definitions Definitions 3 forms for a quad. function 3 forms for a quad. function Steps for graphing each form.

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

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 +

Quadraticsparabola (u-shaped graph) y = ax2 y = -ax2 Sketching Quadratic Functions A.) Opens up or down: 1.) When "a" is positive, the graph curves upwards.

 Determine the maximum value of the quadratic relation: y = -3x x + 29  We can’t factor this, so what do we do?  Look for the axis of symmetry,

1.1 Graphing Quadratic Functions (p. 249)

Do Now: 1.Find the axis of symmetry: 2. See page 176 and do #19 Student will be able to transform a quadratic equation in standard form to vertex form.

1 Introduction to Chapter 5 Chapter 5 – Quadratic Functions 1. Four ways to solve them 2. How to graph quadratic functions and inequalities Remember! Bring.

5.1 Graphing Quadratic Functions Do now: Make up three examples of linear functions. How do you know they are linear? OBJ: to graph quadratic functions.

Graphs of Quadratic Equations. Standard Form: y = ax 2 +bx+ c Shape: Parabola Vertex: high or low point.

Do Now Time (hours)02357 Height (millimeters) John placed a container outside during a rainstorm. A gauge on the side of the container shows the.

Algebra 2 (Section 4.9).

Unit 10: Introduction to Quadratic Functions Foundations of Mathematics 1 Ms. C. Taylor.

Graphing Quadratic Equations in Vertex and Intercept Form

Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you graph quadratic functions in vertex form? Standard:

Do Now 1.Factor: f(x) = 3x x Factor f(x) = 2x 2 - 7x + 3.

Graphing Quadratic Functions

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

5.1 Graphing Quadratic Functions (p. 249) What does the graph of a quadratic function look like? What are the major parts of a quadratic function? How.

Quadratic Functions and their Graphs If a graph has an axis of symmetry, then when you fold the graph along this axis, the two halves of the graph coincide.

GRAPHING QUADRATIC FUNCTIONS

Chapter 6-1 Graphing Quadratic Functions. Which of the following are 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.

Algebra II Elements 5.2: Graph quadratic function in vertex or intercept form HW: p.232 (36-48 even) Tomorrow: projects are due, midterm review.

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

Fri 12/11 Lesson 4 – 1 Learning Objective: To graph quadratic functions Hw: Graphing Parabolas Day 1 WS.

1 Solving Quadratic Equations 1Shaw 2008 February 16, 2010.

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

9.1 Graphing Quadratic Functions. Quadratic Function A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. A function.

2.2 Graphing Quadratic Functions Definitions 3 forms for a quad. function Steps for graphing each form Examples Changing between eqn. forms.

3.2 Graphing Quadratic Functions in Vertex or Intercept Form Definitions Definitions 3 Forms 3 Forms Steps for graphing each form Steps for graphing each.

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

5.8 Modeling with Quadratic Functions

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

Warm Up  1.) What is the vertex of the graph with the equation y = 3(x – 4) 2 + 5?  2.) What are the x-intercepts of the graph with the equation y= -2(x.

5.1 Graphing Quadratic Functions (p. 249) Definitions Definitions 3 forms for a quad. function 3 forms for a quad. function Steps for graphing each form.

Warm Up. CCGPS Geometry Day 37 ( ) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: How do we graph.

Homework. Quadratic Function A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. A function of the form y=ax 2 +bx+c.

Daily Check 1.Factor: 3x x Factor and Solve: 2x 2 - 7x + 3 = 0.

4.1 and 4.2 Graphing Quadratic Functions Definitions Definitions 3 forms for a quad. function 3 forms for a quad. function Steps for graphing each form.

4.1/4.2 Graphing Quadratic Functions in Vertex or Intercept Form Definitions Definitions 3 Forms 3 Forms Steps for graphing each form Steps for graphing.

5.1 Graphing Quadratic Functions Copy the notes from each slide of this power point into your notes section, including graphs. Complete the in-class practice.

Graphing Quadratic Functions

Algebra 2 Name:_____________________

3.3 Quadratic Functions Quadratic Function: 2nd degree polynomial

5.1 Graphing Quadratic Functions (p. 249)

5.1 Graphing Quadratic Functions (p. 249)

3.2 Graphing Quadratic Functions in Vertex or Intercept Form

Graphing Quadratic Functions in Vertex or Intercept Form

Graphing Quadratic Functions In Vertex Form

3.2 Graphing Quadratic Functions in Vertex or Intercept Form

GRAPHING QUADRATIC FUNCTIONS

9.1 Graph Quadratic Functions Alg. I

Daily Check Factor: 3x2 + 10x + 8 Factor and Solve: 2x2 - 7x + 3 = 0.

9.1 Graphing Quadratic Functions

Graphing Quadratic Functions

Daily Check Factor: 3x2 + 10x + 8 Factor and Solve: 2x2 - 7x + 3 = 0.

Graphs of Quadratic Functions Part 1

Section 2.2 Characteristics of Quadratic Functions

4.1 Graphing Quadratic Functions

4.7A Complete the Square Algebra II.

Graphing Quadratic Functions

Presentation transcript:

4.2A Graph Quadratic Functions in Vertex or Intercept Form Algebra II Algebra II

Vertex Form Equation y=a(x-h)2+k If a is positive, parabola opens up If a is negative, parabola opens down. The vertex is the point (h,k). The axis of symmetry is the vertical line x=h. Don’t forget about 2 points on either side of the vertex! (5 points total!)

Example 1: Graph y=-.5(x+3) 2 +4 a is negative (a = -.5), so parabola opens down. a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Axis of symmetry is the vertical line x = -3 Table of values x y Table of values x y Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

Now you try one! Ex. 2 y=2(x-1) 2 +3 Open up or down? Open up or down? Vertex? Vertex? Axis of symmetry? Axis of symmetry? Table of values with 5 points? Table of values with 5 points?

(-1, 11) (0,5) (1,3) (2,5) (3,11) X = 1

Intercept Form Equation y=a(x-p)(x-q) The x-intercepts are the points (p,0) and (q,0). The x-intercepts are the points (p,0) and (q,0). The axis of symmetry is the vertical line x= The axis of symmetry is the vertical line x= The x-coordinate of the vertex is The x-coordinate of the vertex is To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. If a is positive, parabola opens up If a is positive, parabola opens up If a is negative, parabola opens down.

Example 3: Graph y=-(x+2)(x-4) Since a is negative, parabola opens down. The x-intercepts are (-2,0) and (4,0) To find the x-coord. of the vertex, use To find the y-coord., plug 1 in for x. Vertex (1,9) The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex)The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex) x=1 (-2,0)(4,0) (1,9)

Now you try one! Ex. 4 y=2(x-3)(x+1) Open up or down? Open up or down? X-intercepts? X-intercepts? Vertex? Vertex? Axis of symmetry? Axis of symmetry?

(-1,0)(3,0) (1,-8) x=1

4.2B Changing from vertex or intercepts form to standard form The key is to FOIL! (first, outside, inside, last) The key is to FOIL! (first, outside, inside, last) Ex 1: y=-(x+4)(x-9)Ex 2: y=3(x-1) 2 +8 Ex 1: y=-(x+4)(x-9)Ex 2: y=3(x-1) 2 +8

Ex 1: y=-(x+4)(x-9) Ex 2: y=3(x-1) 2 +8 =-(x 2 -9x+4x-36) =3(x-1)(x-1)+8 =-(x 2 -5x-36) =3(x 2 -x- x+1)+8 =-(x 2 -5x-36) =3(x 2 -x- x+1)+8 y=-x 2 +5x+36 =3(x 2 -2x+1)+8 Min. or max. ? =3x 2 -6x+3+8 y=3x 2 -6x+11 y=3x 2 -6x+11 Min. or max?

Assignment