Download LESSON 3.2: COMPLEX NUMBERS --Simplify imaginary numbers

PORTFOLIO PAGE – QUADRATIC EQUATIONS (CH 3)
Lesson 3.1: Solving Quadratic Equations
--by factoring, graphing, and square roots
1)
2)
3)
4)
TO SOLVE QUADRATIC EQUATIONS BY FACTORING:
Write equations in standard form (set = to zero)
Factor
Apply zero product property and set each variable factor to zero.
Solve the equations
1) x2 = 16x – 48
HONORS ALGEBRA 2
2) 9x2 – 16 = 0
TO SOLVE BY FINDING SQUARE ROOTS:
1) Isolate squared term on one side of equation
2) Take the square root of each side. *don’t forget
±
3)
x2 – 5x + 2 = 0
TO SOLVE BY GRAPHING:
1) Graph the related function y = ax2 + bx + c
2) Find ZEROS (x-intercepts): 2nd/CALC/Zero
Left bound, Right bound, Guess
LESSON 3.2: COMPLEX NUMBERS
--Simplify imaginary numbers --Perform operations on complex numbers
Lesson 5-7: Solving Quadratic Equations
Complex
Complex numbers: The set of complex numbers is made up of imaginary and real
numbers combined. A complex number is written in the form a + bi, where a and b are
real numbers, including zero.
#s
Real
Rational
Imaginary
Pure imaginary numbers are numbers of the form 0 + bi where b ≠ 0
Irrational
Simplify:
1) −32 − 5
i = −1
i2 = -1
i3 = -i
i4 = 1
An imaginary number is any number of the form a + bi, where b ≠ 0
2) (5-3i)(4+2i)
Solve:
5) -3x2 – 5 = 0
3) 3i19
4) 3i – (6 – i)
5) 3i3(4 – 11i)
6) -3(x – 2)2 = 8
LESSON 3.3: SOLVING QUADRATIC EQUATIONS
-By Completing the Square
1)
2)
3)
4)
5)
6)
STEPS TO SOLVING EQUATIONS BY COMPLETING THE SQUARE
Get x terms on one side in descending order and the constant term on the other
--By
Completing
Square
Divide (if necessary) to get
a coefficient
of 1the
on the
squared term
Add the number needed to complete the square to both sides
Write one side as a binomial square, simplify the other
Take square root of each side
Solve for x.
Solve:
2x2 – 6x + 8 = 0
-x2 + 8x = -4
M. Murray
LESSON 3.4: QUADRATIC FORMULA
--Solve quadratic equations using Quadratic Formula --Use discriminant to determine # and
type of solutions
QUADRATIC
FORMULA
*equation must FIRST be in standard
form ax2 + bx + c = 0
−𝑏 ± 𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
Solve:
1)
4x2 = -x – 5
THE DISCRIMINANT: Finding # and Type of Solutions:
The radicand b2 – 4ac is called the discriminant
If b2 – 4ac > 0, the equation has _____ _________
solution(s).
If b2 – 4ac = 0, the equation has _____ _________
solution(s).
If b2 – 4ac < 0, the equation has _____ __________
solution(s).
State the number and type of solutions to the
following WITHOUT SOLVING:
4) 3x2 – 8x + 5 = 0
2)
2x2 + 2 = 5x
5) 5x2 = x – 3
6) -6x + 9 = -x2
3) Write a quadratic equation that has the
given solution: x =
−4± −124
−14
7) Find a possible pair of integer values for a
and c so that the quadratic equation ax2 – 6x +
c has one real solution.
Falling Object Model: h = -16t2 + h0; h is height in feet, t is time in seconds, h0 is initial height
Students designed a container that prevents an egg from breaking when dropped from a height
of 80 feet. Write a function that gives the height h (in feet) of the container after t seconds.
How long does it take the container to hit the ground? Find and interpret h(1) – h(1.5)
Write and solve an equation to find two consecutive odd integers whose product is 143.
M. Murray