Quadratic Formula
7
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Transcript of Quadratic Formula
Solving Quadratic Equations using the Quadratic Formula
Page 3
General equation of a quadratic: 02 cbxax
Quadratic Formula:
a
acbbx
2
42 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.
You must get equation equal to zero before you determine a,b, and c.
#10: 01382 xx Page 3
13
8
1
c
b
a
a
acbbx
2
42
12
131488 2 x
2
128x
3412
32 2
328x
34x
Before you can find a,b, and c, you must get equation = to 0.
Type what is under the radical exactly as written on your calculator.
Simplify the radical
Divide by the denominator, if you can
Roots:
Page 3#14: 053 2 x
5
0
3
c
b
a
a
acbbx
2
42
32
53400 2 x
6
600x
6
152x
15460
152
3
15x
Simplify the radical
Divide by the denominator, if you can. Since I can’t, divide by GCF
Roots:
Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form.
Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth.
Page 3#16: 029122 xx
29
12
1
c
b
a
a
acbbx
2
42
12
29141212 2 x
2
2812x
Since we are solving to the nearest tenth, we do not need to simplify the radical!
2
2812x
2
2812 x
64.8x6.8x
35.3x4.3x
Be careful when typing this into your calculator. I recommend that you type in the numerator then hit enter, then divide by denominator!
Roots:
Page 3#25: xx 1082
8
10
1
c
b
a
a
acbbx
2
42
12
8141010 2 x
2
6810x
x10 x10
08102 xxSolve the quadratic equation by using the quadratic formula and round answers to the nearest tenth.
2
6810x
2
6810 x
12.9x1.9x
87.x9.x
Roots:
Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth.
Page 3#25: 123 xx163 2 xx
1 1
0163 2 xx
1
6
3
c
b
a
a
acbbx
2
42
32
13466 2 x
6
486x
6
486x
6
486 x
15.2x1.2x
15.x2.x
Roots
Page 3
Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form.
#25: xx 412 2 x4 x4
0142 2 xx
1
4
2
c
b
a
a
acbbx
2
42
22
12444 2 x
4
84x
248
224
224x
Divide by the denominator, if you can. Since I can’t, divide by GCF
2
22x
Roots:
