daily check for each equation find the discriminant and the number of solutions
TRANSCRIPT
Daily Check
For each equation find the discriminant and the number of solutions.
21. 3 4 2 0x x
22. 6 9 0x x
Launched Object
h(t) = -16t2 + 64t + 80
a) How many seconds until the max height is reached?
b) What will be the max height?
c) How many seconds until the object hits the ground?
2 sec.
144 ft.
5 sec.
Math IDay 10 (8-24-09)
UNIT QUESTION: What is a quadratic function?Standard: MM2A3, MM2A4
Today’s Question:How do we take the square root of negative numbers?Standard: MM2N1.a, b, c, d
2
2
2
i1i
• You can't take the square root of a negative number, right?
• When we were young and still in Math I, no numbers that, when multiplied by themselves, gave us a negative answer.
• Squaring a negative number always gives you a positive. (-1)² = 1. (-2)² = 4 (-3)² = 9
So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary”
1i
So, does
1really exist?
Examples of how we use
1i
16 16 1
4 i 4i
81 81 1
9 i 9i
Examples of how we use
1i
45 45 1
3 3 5 1
3 5 1
3 5 i
3 5i
2 2 2 5 5 1
200 200 1
2 5 2 1
10 2 i
10 2i
2
3
4
5
i
i
i
i
Ex: Solve x2+ 6x +10 = 0
a
acbbx
2
42
a =
b =
c =
26 6 4 1 10
2 1
1st
6 36 4 1 10
2 1
2nd 6 36 40
2
6 4
2
6 2
2
i
6 2 6 2
2 2
i iand
3 3i and i
Complex Numbers
A complex number has a real part & an imaginary part.
Standard form is:
bia
Real part Imaginary part
Example: 5+4iExample: 5+4i
The Complex Plane
Imaginary Axis
Real Axis
Graphing in the complex plane
i34 .
i52 .i22 .
i34
.
Adding and Subtracting(add or subtract the real parts, then add or subtract the imaginary parts)
Ex: )33()21( ii )32()31( ii
i52
Ex: )73()32( ii (2 3 ) ( 3 7 )i i
i41
Ex: )32()3(2 iii )32()23( iii
i21
Graphing in the complex plane
i34 .
i52 .i22 .
i34
.
Absolute Value of a Complex Number
The distance the complex number is from the origin on the complex plane.
If you have a complex number
the absolute value can be found using:
) ( bia
22 ba
Graphing in the complex plane
i52 .2
5
Examples
1. i52
22 )5()2(
254 29
2. i622 )6()0(
360
366
Which of these 2 complex numbers is closest to the origin? -2+5i
Try These!!!
1. 4 i
2 2(4) ( 1)
16 1 17
2. 3i2 2(0) (3)
0 9
93
Which of these 2 complex numbers is closest to the origin? 3i
Practice
Coach Workbook Page 21
Assignment
Page 4 #16-21
Page 8 #6-10
Page 19 #1-10