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Pop Quiz: Take out a piece of paper. Do
NOT put your name on it, only your
student ID. Number 1-6.
Factor:
2
1) 3x -6x-24
3)
2
64x -25
5)
2
2x -50
`
2) x2+3x-54
4)
2
3x +5x-12
6)
2
4x +17x-15
WARM UP: Factor!
2
a) 25b - 20b
5b (5b - 4)
2
b) 5x - 5x - 10
5 (x + 1)(x - 2)
(Hint: Factor a GCF first)
2
c) 28x + 13x - 6
(4x + 3)(7x - 2)
4.5 SOLVING QUADRATIC EQUATIONS
Why do we need to solve quadratic equations?
STEP #1 - For every quadratic equation,
SET = 0
Example 1: Set the following equations = 0.
2
a) 5x + x = 4
2
b) x = 4x + 8
2
c) 2x = 8x
Example 2: Solve the following equations by graphing
2
a) x + 18 = 9x
b) x2 - 4x = 0
2
c) x + 6x = - 9
d) 3x2 - 5x - 4 = 0
(Round to 2 decimal places)
2
c) x + 6x = - 9
2
d) 3x - 5x - 4 = 0
(Round to 2 decimal places)
Example 3: Try to find the solutions of the following equations
by graphing. Hints include how many solutions there are.
2
a) x - 10x + 25 = 0
(1 solution)
2
b) x + 5x + 3 = 0
(2 solutions)
2
c) x = 4x + 8
(2 solutions)
Example 4:
What are the roots of this
equation?
Example 5:
What are the zeroes of this graph?
How many real roots?
What are the zeroes?
Vertex
Axis of symmetry
Example 6: Solving by Graphing OR Factoring
An arrow was shot from the surface of the moon following the
path of 2x2 - 8x, where x is the # of seconds since the arrow
was shot.
How long was the arrow in the air?
Example 7: Solve the following equations by factoring:
2
a) x + 6x + 8 = 0
2
b) 2x + 6x = -4
c) 3x2 = 16x + 12
Example 8: Try to solve the following equations by factoring:
a) x2 - 10x + 25 = 0
2
b) 2x + 6x = - 4
2
c) 6x + 4x = 0
Quiz Thursday:
a) Graphing a quadratic equation
i) Be able to identify vertex, axis of
symmetry, roots/zeros, domain,
range
b) Factoring of all types
c) Solving by factoring/Solving by
graphing
Factoring Match
Arrange the squares in a 4x4 square so
that equivalent expressions match. The
handwritten numbers in the middle mean
NOTHING.
First 4 groups to finish
add 5% to their quiz.