Warm Up

A dance club charges a $5 cover charge when the regular dj plays. The manager estimates that each

$.50 increase in cover charge will decrease attendance by 10 people, and each $.50 decrease

will increase attendance by 10 people. Currently, the average attendance is about 200 people.

Write a function to represent the price, p(x) Write a function to represent the attendance,

a(x) Write a function to represent the revenue, r(x)

Click anywhere when you

finish reading the problem.

Write a function to represent the price, p(x)

Write a function to represent the attendance, a(x)

Write a function to represent the revenue, r(x)

)5.5(or )5.5( xx

)10200(or )10200( xx

10x)(200)5.5(

or

)10200)(5.5(

x

xx

Find what the cover charge should be to maximize revenue and what the maximum revenue is

Solving Quadratic Equations by Squaring

• When solving an equation by squaring both sides, look for extraneous solutions

Example

53 x

2253 x

253 x28x

5328 525

55

CHECK

IT

Since this is a FALSE

statement, it is called an

extraneous solution

Here’s a HINT!

If my constant is negative, there

is NO SOLUTION!

Solve for x.

73 x 22

73 x

493 x46x

7346 749 77

Another ExampleSolve for x.

1244 x

221244 x

14444 x1404 x

124)35(4

124140 12144

35x

1212

One More…You know it..solve for x.

x315 x5

225 xx25

25315 5315 1515 Alright, let me

try some!

Example 1

2x

Example 1-Answer

2x 22

2x

4x

22

24

Since we got a

FALSE statement, this is an

EXTRANEOUS SOLUTION!!

That was too easy. Try Another!

Example 2

61532 x

Example 2-Answer

61532 x3153 x

223153 x

9153 x243 x

8xTry Another!

Example 3

543 x

Example 3

3

1

13

13

13

543

22

x

x

x

x

x

Last Thing!

Pythagorean TheoremDistance formula

Distance Formula

212

212 yyxxd

Here’s an example!

(4,3) and (1,2)

:points twoebetween th distance theFind

1.310

19

1)3(

2314

22

22

d

I’d like to try!

Distance Formula Example

(-1,-3) and (4,-3)

:points twoebetween th distance theFind

Distance Formula Answer

(-1,-3) and (4,-3)

:points twoebetween th distance theFind

5

25

0)5(

3341

22

22

d

Pythagorean Theorem222 cba

Only used in RIGHT

TRIANGLES!10 is c 6, is a

ABC, oflength side missing theFind

8

64

10036

106

2

2

222

b

b

b

b

My answer is not because side length CANNOT be negative!

I’d like to try!

Pythagorean TheoremExample

2 is b 9, is a

ABC, oflength side missing theFind

Pythagorean TheoremAnswer

2 is b 9, is a

ABC, oflength side missing theFind

2.985

85

481

29

2

2

222

c

c

c

c

GET YOUR HOMEWORk

NOW!!!