Nuffield Free-Standing Mathematics Activity

Slides:

Advertisements

Similar presentations

Vocabulary axis of symmetry standard form minimum value maximum value.

Advertisements

Means writing the unknown terms of a quadratic in a square bracket Completing the square Example 1 This way of writing it is very useful when trying to.

Quadratic Equations A quadratic is any expression of the form ax 2 + bx + c, a ≠ 0. You have already multiplied out pairs of brackets and factorised quadratic.

© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Completing the square.

Quadratic Graph Drawing.

12-4 Quadratic Functions CA Standards 21.0 and 22.0 CA Standards 21.0 and 22.0 Graph quadratic functions; know that their roots are the x-intercepts; use.

©2007 by S – Squared, Inc. All Rights Reserved. **RECALL**  Quadratic Function in general form: ax 2 + bx + c where a, b, and c are real number coefficients.

Quadratic Theory Introduction This algebraic expression: x 2 + 2x + 1 is a polynomial of degree 2 Expressions like this in which the highest power of x.

Solve Using Best Method

1Higher Maths Quadratic Functions. Any function containing an term is called a Quadratic Function. The Graph of a Quadratic Function 2Higher Maths.

1. Determine if f(x) has a minimum or maximum 2. Find the y-intercept of f(x) 3. Find the equation of the axis of symmetry of f(x) 4. Find the vertex of.

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.

Goal: Graph quadratic functions in different forms.

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

Sketching quadratic functions To sketch a quadratic function we need to identify where possible: The y intercept (0, c) The roots by solving ax 2 + bx.

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.

Graphing Quadratic Functions (2.1.1) October 1st, 2015.

Reminders (1) The graph of a quadratic function is a parabola. If a > 0 the parabola isshaped and the turning point is a minimum. If a < 0 the parabola.

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

4-2 Quadratic Functions: Standard Form Today’s Objective: I can graph a quadratic function in standard form.

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.

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.

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

Section 8.7 More About Quadratic Function Graphs  Completing the Square  Finding Intercepts 8.71.

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.

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

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

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

A quadratic function always contains a term in x 2. It can also contain terms in x or a constant. Here are examples of three quadratic functions: The.

Factor each polynomial.

Quadratic Functions Unit Objectives: Solve a quadratic equation.

Quadratic Functions, Quadratic Expressions, Quadratic Equations

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

Warm Up /31/17 1. Evaluate x2 + 5x for x = 4 and x = –3. __; ___

Quadratic Functions and Their Properties

Quadratic Equations Chapter 5.

Using the Vertex Form of Quadratic Equations

Quadratic Graph Drawing.

Solving Quadratic Equations by Graphing

Warm-up Solve by factoring: 3x2 – 16x – 7 = 5

Solving a Quadratic Equation by Graphing

Completing the square means writing the unknown terms of a quadratic in a square bracket Example because Application To find the maximum or minimum value.

Quadratic Functions.

Blue Book 16 Quadratic Graphs.

3.1 Quadratic Functions and Models

Graphing Quadratic Functions (2.1.1)

Nuffield Free-Standing Mathematics Activity

Section 9.1 Day 4 Graphing Quadratic Functions

The Discriminant CA 22.0, 23.0.

Review: Simplify.

Creating & Graphing Quadratic Functions Using Standard Form (3.3.1)

Section 9.1 Day 2 Graphing Quadratic Functions

Section 9.1 Day 3 Graphing Quadratic Functions

Graphs of Quadratic Functions

Some Common Functions and their Graphs – Quadratic Functions

3.1 Quadratic Functions and Models

Linear and Quadratic Functions

Obj: graph parabolas in two forms

Quadratic Graph Drawing.

4.1 Notes – Graph Quadratic Functions in Standard Form

Algebra 2 – Chapter 6 Review

Quadratic Equation Day 4

QUADRATIC FUNCTION PARABOLA.

Quadratic Graph Drawing.

Q1: Student has difficulty starting

Presentation transcript:

Nuffield Free-Standing Mathematics Activity Completing the square

Completing the square means writing the unknown terms of a quadratic in a square bracket Example because Application To find the maximum or minimum value of this function. Think about… What is always true about the value of (x + 3)2? What will always be true for (x + 3)2 – 2? Minimum value of is –2

Application To find the minimum point on the graph of the function. Think about… For what value of x is (x + 3)2 – 2 a minimum? has a minimum value when x = –3 Minimum point on the curve is (–3 , –2) Think about… What shape is the graph of y = x2 + 6x + 7 ? Can completing the square help you sketch the graph of a quadratic?

Graph of y = x2 + 6x + 7 line of symmetry y x x = –3 Minimum point 7 is (–3 , –2) x = –3 is a line of symmetry When x = 0, y = 7 (–3, –2) So the intercept on the y axis is 7

Example Think about… What is the maximum or minimum value? Think about… What shape will the graph be? Where is its turning point? To sketch the graph of line of symmetry y x has a minimum value when x = 1 5 Minimum point is (1, 3) (1, 3) Intercept on the y axis is 5 x = 1

Example Think about… What is the maximum or minimum value? Think about… What shape will the graph be? Where is its turning point? To sketch the graph of y x (–2, 7) x = –2 has a maximum value when x = –2 Maximum point is (–2, 7) 3 Intercept on the y axis is 3 Note you can find the intercepts on the x axis by solving

Completing the square Reflect on your work How does completing the square help you to sketch the graph of the function? Can you use completing the square to tell you whether the quadratic function has any real roots?