The document discusses solving quadratic equations using the quadratic formula. It provides the general form of a quadratic equation as ax2 + bx + c = 0 and introduces the quadratic formula as x = (-b ± √(b2 - 4ac))/2a. Several examples of using the quadratic formula to solve quadratic equations are shown step-by-step with explanations of each step. The examples illustrate determining the a, b, and c coefficients and performing the calculations to find the roots of the equations.

1. Solving Quadratic Equations
using the Quadratic Formula
General equation of a quadratic:
ax 2 bx c 0
Quadratic Formula:
x
b
b2
2a
4ac
Page 3
You must get equation
equal to zero before you
determine a,b, and c.
Notice where the
letters come from for
the formula
We use the quadratic formula when something can not be factored.
However, it also works for factorable quadratic equations as well.

2. #10:
x
2
8 x 13 0
a 1
b
8 x
b2
2a
b
c 13
8
x
8
21
x
12
Before you can find
a,b, and c, you must
get equation = to 0.
4 3
x
2 3
x
2
4ac
12
2
Simplify the radical
8 2 3
2
4
Type what is under
the radical exactly as
written on your
calculator.
4 1 13
8
Page 3
Divide by the denominator, if you can
3
Roots:

3. a 3
b 0
c
b2
2a
b
x
5
0
43
23
0
x
4 15
2 15
x
5
60
6
x
Solve the quadratic equation by using
the quadratic formula and leave
answers in simplest radical form.
4ac
2
0
x
60
Page 3
3x 2 5 0
#14:
2 15
6
15
3
Simplify the radical
Divide by the denominator, if you
can. Since I can’t, divide by GCF
Roots:

4. #16: x
2
a 1
b
12 x
c
b2
2a
b
29
12
x
12
28
2
x 8.64
x 8.6
12
Solve the quadratic equation by
using the quadratic formula and
round answers to the nearest tenth.
4ac
12
21
x
x
Page 3
12 x 29 0
2
4 1 29
Since we are solving to the nearest
tenth, we do not need to simplify
the radical!
28
2
x
12
28
2
x 3.35
x 3.4
Be careful when typing this into
your calculator. I recommend that
you type in the numerator then hit
enter, then divide by denominator!
Roots:

5. x 2 8 10 x
10x 10x
#25:
x
2
Solve the quadratic equation by
using the quadratic formula and
round answers to the nearest tenth.
10x 8 0
a 1
b
10
b
x
c 8
10
x
x
Page 3
10
2
b2
2a
4ac
2
10
21
10
68
x
2
68
10
x
x 9.12
x 9.1
41 8
68
2
x .87
x .9
Roots:

6. 3x x 2
#25:
1
Page 3
3x 2 6 x 1
1
1
Solve the quadratic equation by
using the quadratic formula and
round answers to the nearest tenth.
3x 2 6 x 1 0
a
b
c
x
3
6
b2
2a
b
x
4ac
x
1
6
x
6
23
6
2
43
1
6
48
x
6
x 2.15
x 2.1
Roots
48
6
x
x
48
6
6
.15
.2

7. #25:
2x2
a
b
2x2 1 4x
4x
4x
4x 1 0
8
Solve the quadratic equation by using
the quadratic formula and leave
answers in simplest radical form.
2
4
x
b2
2a
b
c 1
x
Page 3
4
4 2
2 2
4
22
x
x
2
4ac
x
42 1
4
2
2
2
Roots:
8
4
4 2 2
4
Divide by the denominator, if you
can. Since I can’t, divide by GCF