Quiz: Take out a piece of paper. Do
NOT put your name on it, only your
student ID. Number 1-6.
Factor:
1) 3x2-6x-24
2) x2+3x-54
3) 64x2-25
4) 3x2+5x-12
5)
2
2x -50
6)
2
4x +7x-15
1. 3(x - 4)(x + 2) or (3x-12)(x+2) or
(3x+6)(x-4)
2. (x+9)(x-6)
3. (8x-5)(8x+5)
4. (3x-4)(x+3)
5. 2(x-5)(x+5)
6. (4x - 5)(x+3)
WARM UP: Factor!
a) 25b2 - 20b
5b (5b - 4)
b) 5x2 - 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
a) x2 + 18 = 9x
2
b) x - 4x = 0
c) x2 + 6x = - 9
d) 3x2 - 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 7: Solve the following equations by factoring:
a) x2 + 6x + 8 = 0
b) 2x2 + 6x = -4
2
c) 3x = 16x + 12
Quiz Thursday:
a) Graphing a quadratic equation
i) Be able to identify vertex, axis of
symmetry, roots/zeros
b) Factoring of all types
c) Solving by factoring