Quadratic Graphs and the Quadratic Formula
2
−
b
±
b
−
4
ac
Given the quadratic formula
x
=
, we can find the x-intercepts of
2
a
quadratic equations that would otherwise be close to impossible to find by factoring
2
alone. For example, examine the equation
0
=
x
+
4
x
+
2
. Using the quadratic formula,
we get the following:
2
4
4
4
1 (
)(
) 2
−
±
−
4
16
8
4
8
−
±
−
−
±
x
=
=
=
2
) 1 (
2
2
We’ll estimate the value of 8 as approximately 2.828, so
4 ±
. 2
828
−
x
therefore
≈
2
4
. 2
828
. 1
172
−
+
−
x
. 0
586
or
≈
=
=
−
2
2
−
4
−
. 2
828
−
. 6
828
x
≈
=
=
−
. 3
414
2
2
Find the x- and y-intercepts of the following quadratic equations. Check your answer
on MathGV.
2
2
1.
2
3
5
2.
3
6
y
=
x
−
x
−
y
=
−
x
+
x
+
2
2
3.
4
2
3
4.
5
3
1
y
=
x
+
x
−
y
=
−
x
−
x
+