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```					Solving Quadratic
Functions

Lesson 5-3
Objective
• Today, you will . . .

• solve quadratic functions by using a
variety of methods.

TEKS:b2A,d1A,d3A,d3C,d3D
Some Notes on
1. The graphs of quadratic functions are
parabolas.
2. The solution(s) that you will be looking for are
the x-intercepts of the parabola.
3. The x-intercepts are also called the “roots,”
“solutions,” or the “zeros”
4. Quadratic functions can have one, two, or
no real solutions.
5. Quadratic functions that have no real
solutions have complex (imaginary)
solutions.
Two real solutions

X=-6
X=1

x-intercepts, roots, zeros
One real solutions

X=3

x-intercept, root, zero
No real solutions

No
Solution
No x-intercepts (roots or
zeros)
Today you’ll find…

equations by factoring

• For example:

GIVEN: y = Ax2 + Bx + C
FIND: The solutions, roots, zeros,
or x-intercepts
Solve by factoring: x2 + 9x + 20 = 0
1 x 20
x2+ 9x + 20 = 0            2 x 20
4x5
(x + 5)(x + 4) = 0
x+5=0                x+4=0
x=-5                  x=-4
So, its two roots, solutions, zeros

are      -5 & -4
Solve by factoring: x2 = -7x + 18

x2   + 7x - 18 = 0                1 x 18
2x9
Hint: The sign of “B” goes with
3x6
the largest factor!
(x - 2)(x + 9) = 0
x-2=0          x+9=0
x=2            x=-9
So, its two roots, solutions, zeros

are        2 & -9
Solve by factoring: x2 + 100 = 29x
1 x 100

x2   - 29x + 100 = 0           2 x 50
4 x 25
5 x 20
(x - 4)(x - 25) = 0    10 x 10

x-4=0          x - 25 = 0
x=4                   x = 25
So, its two roots, solutions, zeros

are      4 & 25
Solve by factoring: x2 - 9 = 0
1x9
x2
-9=0                     3x3

(x + 3)(x - 3) = 0
x+3=0                   x-3=0
x=-3                     x=3
So, its two roots, solutions, zeros are

-3 & 3
Solve by factoring: x2 + x = 6
1x6
x 2   +x-6=0                    2x3
Hint: The sign of “B” goes with
the largest factor!
(x - 2)(x + 3) = 0
x-2=0          x+3=0
x=2             x=-3
So, its two roots, solutions, zeros

are      2 & -3
Solve by factoring: x2 - 6x = - 8
1x8
x=2            2x4

x=4
Solve by factoring: x2 - 8 = - 7x
x=1             1x8
2x4

x=-8
Solve by factoring: 2x2 + 13x + 15 = 0

2x2 + 13x + 15 = 0             Multiply AxC                 = 30

Determine the factors of 30 that
1 x 30
give you 13
2 x 15
3 x 10

(x + 3) (x + 10)              Write the factors

(x + 3) (x + 10 )             Divide the #’s by A
2        2

(2x + 3) (x + 5)              If not divisible, send it in front of “x”,
if divisible then simplify.
2x + 3 = 0            x+5=0                  Now solve both factors!
2x = -3               x = -5                       Your solutions are
x = -3/2                                          x = -3/2 and x = -5
Solve by factoring: 3x2 + 16x + 21 = 0

3x2 + 16x + 21 = 0             Multiply AxC            = 63

Determine the factors of 63 that
1 x 63
give you 16
3 x 21
7x9

(x + 7) (x + 9)              Write the factors

(x + 7) (x + 9 )             Divide the #’s by A
3       3

(3x + 7) (x + 3)              If not divisible, send it in front of “x”,

if divisible then simplify.
3x + 7 = 0            x+3=0         Now solve both factors!
3x = -7               x = -3                      Your solutions are
x = -7/3                                         x = -7/3 and x = -3
Solve by factoring: 2x2 – 5x = 7

2x2 – 5x – 7 = 0       Multiply AxC                                = -14
Determine the factors of -14 that           1 x 14
give you -5
2x7
(x + 2) (x – 7)     Write the factors
Remember, sign of “B” goes to the largest factor, in this case, the
negative goes to the 7.

(x + 2) (x – 7)         Divide the #’s by A
2       2

(x + 1) (2x – 7)            If not divisible, send it in front of “x”,
if divisible then simplify.

x+1=0               2x – 7 = 0              Now solve both factors!
x = -1              2x = 7                          Your solutions are
x = 7/2                        x = -1 and x = 7/2
Solve by factoring: 5x2 + 4x = 12
5x2 + 4x – 12 = 0               AxC=                    -60
1 x 60 4 x 15
2 x 30   5 x 12
3 x 20   6 x 10
(x – 6) (x + 10)    Write the factors (watch your signs!)

(x – 6) (x + 10)    Divide the #’s by A
5       5
(5x – 6)(x + 2)     If not divisible, send it in front of “x”,
if divisible then simplify.

5x – 6 = 0          x+2=0                Now solve both factors!
5x = 6              x = -2
x = 6/5
x = 6/5 and x = -2
You try these by factoring . . .

1.   2x2 – 3x = 0
x = 0 and 3/2
2.   4x2 + 5 = -9x
x = -1 and -5/4
3.   6x2 + 55x = -9
x = -9 and -1/6

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 views: 19 posted: 10/7/2011 language: English pages: 19
Jun Wang Dr
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