11/7/11 SECTION 7.5
Solve radical equations – not much new – we did this
whenever we used Pythagorean theorem
On May 20th, it has been reported that the snow pack
at Alta has melted 15 centimeters every other day. On
that day the depth of the snow was 355 centimeters.
Describe the depth of the snowpack as it changes with
days passed after May 20th.
•  Where on the graph will you find how deep the snowpack
is on May 20th?
•  How long will it take for the snow to melt completely?
Where can you find this information on the graph?
•  How much snow melts every day? Where can you find
this information on the graph? Can you find it in your
formula?
•  How big was the snow pack on May 5th? Where can you
find this information on the graph?
•  Can you predict what the snow pack was on January 1st?
Why or why not?
1 11/7/11 •  How long will it take for the snow to melt completely?
Where can you find this information on the graph?
•  How much snow melts every day? Where can you find
this information on the graph? Can you find it in your
formula?
•  How big was the snow pack on May 5th? Where can you
find this information on the graph?
•  Can you predict what the snow pack was on January 1st?
Why or why not?
2 11/7/11 Solving equations involving radicals
z −4 =0
−4 y = 4
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3 11/7/11 What is the solution(s) of the equation −4 y = 4 ?
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1. x = 4
2. x = -4
1
3. x =
4
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Solve each equation (Don’t forget to
check your solutions.)
3 − 2x = 2
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€
2x − 7 = −5
3x +1 = t +15
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4 11/7/11 More different equations 
2 3 10 − 3x = 3 2 − x
3x + 7 = x + 3
z + 2 = 1+ z
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Solve each equation (Don’t forget to
check your solutions.)
4 3 x +1
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€
x2 − 4 = x − 2
x + x +2 =2
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5 11/7/11 And then some
A couple was having a romantic get away in a hot air
balloon. They brought their picnic along, and unwittingly
they dropped an egg. The egg strikes the ground with
a velocity of 35 miles per hour. What color was the hot
air balloon? How far off the ground was it when the egg
was dropped?
v = 2gh
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6 11/7/11 SECTION 7.6
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•
•
•
Write the square roots of negative numbers in i-form and perform
operations on them.
Determine the equality of two complex numbers
Add, subtract and multiply complex numbers.
Use complex conjugates to write the quotient of two complex numbers
in standard form.
Complex Numbers
•  Expanding our universe to include…imaginary numbers!
•  Like your imaginary friends, they exist…they’re just not real.
•  It’s just that they live…in another dimension! (Seriously.)
7 11/7/11 Solve these quadratic equations.
Find the x-intercepts of these quadratic
functions.
8 11/7/11 Solve and graph the solution(s).
Solve and graph the solution(s).
9 11/7/11 Imaginary unit
•  If c is a positive real number, then the square root of –c is
given by
Complex numbers
•  If a and b are real numbers then the number a+ib is called
a complex number. The form a+ib is called the standard
form of the complex number.
10 11/7/11 Operations with complex numbers
11 11/7/11 Further examples
SECTIONS 8.1-8.3
Solve quadratic equations by
•  factoring.
•  square root property.
•  completing the square.
•  quadratic formula.
12 11/7/11 Back to solving equations
•  Now we can solve:
Back to solving equations
13 11/7/11 How could we do this:
Completing the square
14 11/7/11 Completing the square
With a twist
15 11/7/11 Few for practice:
3x 2 − 4 x − 5 = 0
4z 2 −3z + 2 = 0
0.5t 2 + t + 2 = 0
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16 11/7/11 I want to put a fence around my garden to keep the dogs out. To
make it easy on myself I’ll make it rectangular. I bought 60 yards
of lattice fence, and I want to use all of it. And, I want the garden
to have area of 250 square yard. Can it be done?
Generalize:
•  We have an equation of the form
•  If we can write it as
then we can solve the equation:
17 11/7/11 Generalize:
•  On the other hand we want to write that equation as
•  So
18