Chapter 5 Quadratics: Make connections between different representations of the quadratic function. You will also solve the quadratic equation using multiple methods.

5.1 Multiple Representations and Description of Students will explore graphs, tables and equations of quadratics. Students will learn and apply the zero product rule to find x-intercepts. Students will solve real world problems.

5.1.1 Graph of a Quadratic When graphing a quadratic function you get a parabola Looks like the letter U Domain is all real numbers Range is limited by the turning Point or vertex

5.1.1 Describing a Parabola Depends on what is given graph, table or equation But you should be able to describe the following Which direction does the parabola open Is it narrow (skinny) or wide (fat) What is the vertex What are the x-interepts Axis of symmetry What is the y-intercept

Based on Graph Opens up (can hold water) or down (won’t hold water) Narrow or Wide – look at distance between sides Vertex – turning point in graph, this should be an ordered pair Axis of symmetry – vertical line through the vertex X-intercepts – order pairs where graph crosses the x-axis, could be 0,1 or 2 Y-intercept – ordered pair where it crosses the y axis only 1

Example Describe the following parabola

Equation Vertex form Factored form Standard form Each form has is pros and cons we will look at throughout this unit

From equation Opens up if a value is positive Opens down if a value is negative Narrow if |a|>1 Wide if |a|<1 We will talk about how to calculate x-intercepts later using multiple methods Vertex – depends on the form given, will talk more about this calculation later Y-intercept sub in zero for x and solve

Calculating Characteristics Vertex The second part of the ordered pair means to sub in the first coordinate into the equation and solve for the second Axis of symmetry X-intercepts try factoring the polynomial

Example Describe what the graph would look like given the equation, graph in calculator to see if you are correct

Homework Worksheet

5.1.2 Connections As a group turn to page 264 read through and work on 5-16 Collect a resource page from the back table to do this Now work through 5-17

5.1.3 Sketch A sketch is being able to plot specific points and connect them These specific points are Vertex – we already discussed how to find Y-intercept – we already discussed how to find X-intercepts – we will use what is called the zero product property, which we have discussed just not named.

Zero Product Property Finding the zeros of a quadratic is the same as finding the x-intercepts What x values would make the equation equal to zero Factor the trinomial completely Set each of the factored parts equal to zero and solve Each part could equal zero separately because when you multiply by zero you will always get zero Ask yourself these questions and we do some problems Did you notice any short cuts Did you notice any thing to determine the number of zeros

Examples

Homework Worksheet

5.1.4 Writing the quadratic equation How can you write an equation given a table of data? How can you write an equation given a graph of the data? As a group work on problem 5-39 on page 273 Try to come up with a process on how to write the equation that represents this table.

Solutions Find the x-intercepts Find the y-intercept Use idea of zero product rule to write out factored form of the quadratic, with x-intercepts Use y-intercept to help determine a value

Example Pg 274 5-40 5-41

Homework Pg 275 5-43 show all work needed to support your answer

5.1.5 Connections As a group work through 5-49 on page 277 Make sure you can explain your choices 5-51 pg 279

Homework Pg 280 5-55