1 What you will learn  How to get a quadratic function from standard form to vertex form  How to solve a quadratic equation using “completing the square”

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Presentation transcript:

1 What you will learn  How to get a quadratic function from standard form to vertex form  How to solve a quadratic equation using “completing the square”

Objective: 5.5 Completing the Square 2 Question?  What are the three different ways we have to graph quadratic functions?  Which do you like best and why?  What about solving a quadratic equation of the form (x – 2) 2 = 25?

Objective: 5.5 Completing the Square 3 Vertex Form  One of the easier methods we had for graphing quadratics was to use the vertex form of the equation: y = (x – 2) Where is the vertex? How do we find more points?

Objective: 5.5 Completing the Square 4 Solving in “Vertex” Form  How do you solve: (x – 3) 2 = 4

Objective: 5.5 Completing the Square 5 Getting a Function into Vertex Form  We will learn how to get a quadratic function into the form that allows us to either graph or solve the equation fairly easily.  The process is called “completing the square”

Objective: 5.5 Completing the Square 6 Another Question  What does x 2 – 8x + 16 factor to? What is this called?  What could we put in for the ? that would allow this to be a perfect square? x 2 – 6x + ?

Objective: 5.5 Completing the Square 7 Mathematical Method for Completing the Square  Find the value of c that makes x 2 – 7x + c a perfect square trinomial. Step 1: Take the b term and divide it by 2: Step 2: Square the result from Step 1. That is your c value! What does it factor to?

Objective: 5.5 Completing the Square 8 You Try  Find the value of c that makes x 2 – 3x + c a perfect square trinomial. Then write the expression as the square of a binomial (factor).

Objective: 5.5 Completing the Square 9 Using this Fun Little Trick  Solve x x – 3 = 0 by completing the square.

Objective: 5.5 Completing the Square 10 You Try  Solve x 2 + 6x – 8 = 0 by completing the square.

Objective: 5.5 Completing the Square 11 What if the x 2 Term Has a Coefficient?  Solve 3x 2 – 6x + 12

Objective: 5.5 Completing the Square 12 Modeling with Quadratics  On dry asphalt the distance d (in feet) needed for a car to stop is given by d = 0.05s s What speed limit should be posted on a road where drivers round a corner and have 80 feet to come to a stop.

Objective: 5.5 Completing the Square 13 Writing Functions in Vertex Form  We can convert from y = ax 2 + bx + c to y = (x – h) 2 + k by completing the square. Example: Write the quadratic function y = x 2 – 8x + 11 in vertex form.

Objective: 5.5 Completing the Square 14 You Try  Write the quadratic function: y = x 2 + 6x + 16 in vertex form and graph it!

Objective: 5.5 Completing the Square 15 Homework Homework 1: page 286, even Homework 2: page 287, even, all, even, 86, 88, 90