Quadratic Equations Worksheet
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816.1 Square Root Property
Introduction to Quadratic Equations
A quadratic equation is any equation that can be written in the standard form
+
+
=
2
ax
bx
c
0
where a,b, and c are real numbers and a > 0. In other words, a quadratic equation is
2
any equation with a polynomial of degree 2 (
x term). A quadratic equation may
have up to 2 real solutions.
Sample Problem:
Write the quadratic equation in standard form and label a,b,c.
= x
−
2
3
x
5
7
Solution:
The standard form of a quadratic equation must have all terms on one side, and must
have a > 0. We must move everything to one side.
=
−
2
3
x
5
x
7
−
+
=
2
3
x
5
x
7
0
Thus a = 3 , b = –5 , c = 7
Student Practice: Write each quadratic equation in standard form and label a, b, c.
+
=
−
+ x
=
2
2.
x
(
x
) 5
4
x
3
1.
x
8
2
−
+
+
=
2
3.
2
x
x
9
0
We have solved quadratic equations before using the zero factor property. An example is shown
below. However, we will now learn that this method cannot always be used.
− x
=
2
Sample Problem:
Solve for x.
x
5
14
Solution:
We must first write the equation in standard form.
−
=
2
−
=
2
x
5
x
14
(
) 7
( 5
) 7
14
−
−
=
−
=
2
x
5
x
14
0
Check:
49
35
14
−
+
=
=
(
x
7
)(
x
) 2
0
14
14
−
7 =
+
2 =
x
0
x
0
=
=
2 −
x
7
x
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