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)2 + 4

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 x2 – 8x + 16 factor to? What

is this called?

What could we put in for the ? that would allow this to be a perfect square?

x2 – 6x + ?

Objective: 5.5 Completing the Square

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Mathematical Method for Completing the Square

Find the value of c that makes x2 – 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 x2 – 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 x2 + 10x – 3 = 0 by completing the

square.

Objective: 5.5 Completing the Square

10

You Try Solve x2 + 6x – 8 = 0 by completing the

square.

Objective: 5.5 Completing the Square

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What if the x2 Term Has a Coefficient? Solve 3x2 – 6x + 12

Objective: 5.5 Completing the Square

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Modeling with Quadratics On dry asphalt the distance d (in feet) needed

for a car to stop is given by

d = 0.05s2 + 1.1s

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

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Writing Functions in Vertex Form We can convert from y = ax2 + bx + c to

y = (x – h)2 + k by completing the square.

Example: Write the quadratic function y = x2 – 8x + 11 in vertex form.

Objective: 5.5 Completing the Square

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You Try Write the quadratic function:

y = x2 + 6x + 16in vertex form and graph it!

Objective: 5.5 Completing the Square

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Homework

Homework 1: page 286, 24-42 even

Homework 2: page 287, 48-52 even, 63-70 all, 74-80 even, 86, 88, 90