Transcript 9-4A Quadratic Formula

Warm Up Use a calculator to evaluate.
Round the results to the nearest hundredth.
Practice 1
Practice 2
Practice 3
45 2
8
2 3
3
23 6
4
 1.38,
  0.38
 1.24
 0.09
 2.34
  1.34
9-4A Solving Quadratic Equations
by Using the Quadratic Formula
You will need a calculator for today’s lesson.
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
Today you will solve quadratic equations by using the
quadratic formula:
 b  b2  4ac
x
2a
The quadratic formula is read as “x equals negative b,
plus or minus the square root of b squared minus 4ac,
all divided by 2a.”
The quadratic formula gives the solutions of ax2 + bx + c = 0
in terms of the coefficients a, b, and c.
a  0 and b2  4ac  0
Sing-a-long: Pop Goes the Weasel
 b  b2  4 ac
x
2a
x equals negative b,
plus or minus square root,
b squared minus 4ac,
all over 2a.”
Sing – a – long competition by rows.
The first step in using the quadratic formula is to identify
the values of a, b, and c.
Write the equation in standard form. Identify values of
a, b, and c.
Write problem.
x2  9x  14
Rewrite in standard form.
x2  9x  14  0
Identify values for a, b, and c.
a  1, b  9, c  14
Example 1 Write the equation in standard form.
Identify the values of a, b, and c.
4x2  13x  3
4x2  13x  3  0
a  4, b  13, c  3
Example 2 Write the equation in standard form.
Identify the values of a, b, and c.
x2  4  6x
x2  6x  4  0
a  1, b  6, c  4
Solve the equation. x2  4x  3  0
Identify values for a, b, c.
a  1, b   4, c  3
Write quadratic formula.
 b  b2  4ac
x
2a

  4  
 4 2   413
21

4  16   4 3
2

4  16   12
2
4 4
2
42

2

42
4 2
, 
2
2
6
2


2
2
3, 1
x
Solve 24x2  14x  6. If the solution involves radicals, round to the
nearest tenth.
Rewrite the equation in standard form. 24x2  14x  6  0
Identify values for a, b, c. a  24, b   14, c  6
Write quadratic formula.
 b  b2  4ac
x
2a
  14    14 2   424  6

224 
14  196   96 6

48

14  196  576
48

14  772
48
x
14  772
14  772
, 
48
48
0.9,  0.3
Solve. If the solution involves radicals, round
to the nearest tenth.
Example 3
x2  5x  6  0
Example 4
2x2  3x  8  0
Example 5
 3x2  x  5  0
Round in
the last
step!
Example 3 Solve x2  5x  6  0. If the solution involves radicals,
round to the nearest tenth.
 b  b2  4ac
x
2a

 5 
52   41 6
21

 5  25   4  6
2

 5  25  24
2
 5  49
2
57

2

57
57
, 
2
2
 12
2


2
2
1,  6
x
Solve. If the solution involves radicals, round to the nearest tenth.
Example 4 2x2  3x  8  0
 b  b2  4ac
x
2a
  3   32   42 8

22
3  9   8 8

4
3  9  64

4
3  73

4
3  73
3  73

, 
4
4
2.9,  1.4
Example 5  3x2  x  5  0
 b  b2  4ac
x
2a
 1  12   4 35

2 3
 1  1  125

6
 1  61
6
1  61

6
1  61
1  61

, 
6
6
1.5,  1.1

9-A12 Page 497-499 #9-20,29–31,60-62.
Use a calculator to evaluate 1  2 3 . Round the results to
4
the nearest hundredth.
12 3
( 1 + 2 2nd √ 3 ) ) ÷ 4 =
 1.12
4
and
12 3
nd
√ 3 ) ) ÷ 4 =
  0.62
( 1 - 2 2
4
When evaluating radical expressions that are not
perfect squares, round the answer in the last step.
Keystrokes for
TI-30X IIS
Does your
calculator have
order of
operations?
Use a calculator to evaluate 1  2 3 . Round the results to
4
the nearest hundredth.
12 3
 1.12
1 +
2 X 3 √ = ÷ 4 =
4
and
12 3
3
=
÷
1 4
X
√
=
2
  0.62
4
When evaluating radical expressions that are not
perfect squares, round the answer in the last step.
Keystrokes for
TI-30X A
When using the quadratic formula, it is helpful to change
the value under the radical to addition when simplifying.
Find the value of b2 – 4ac for the equation.
2
2x
 4x  5  0
Write problem.
Identify the values for a, b and c.
Write the expression.
Simplify. (Place values in
parentheses and change
subtraction to addition to
avoid sign errors.)
a  2, b   4, c  5
b2  4ac
 4 2   42 5
16   8 5
16  40
56
Example 3 Find the value of b2 – 4ac for the equation.
3x2  8x  7  0
a  3, b  8, c  7
b2  4ac
 82   43 7 
64   12 7 
64  84
148