Graph of quadratic equations x²-9=0
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Step-by-step explanation:
A quadratic equation is of the form:
a
x
2
+
b
x
+
c
=
0
We have :
y
=
f
(
x
)
=
x
2
−
9
Set
y
=
0
We have the quadratic equation:
x
2
−
9
=
0
Using the algebraic identity:
a
2
−
b
2
≡
(
a
+
b
)
(
a
−
b
)
We can rewrite
x
2
−
9
=
0
as
x
2
−
3
2
=
0
⇒
(
x
+
3
)
(
x
−
3
)
=
0
⇒
(
x
+
3
)
=
0
,
(
x
−
3
)
=
0
⇒
x
=
−
3
,
x
=
3
Hence, there are two solutions for
x
So, we have two x-intercepts:
(
−
3
,
0
)
and
(
3
,
0
)
To find the y-intercept, set
x
=
0
⇒
y
=
(
0
)
2
−
9
=
0
⇒
y
=
−
9
Hence, the y-intercept:
(
0
,
−
9
)
The graph of
y
=
f
(
x
)
=
x
2
−
9
is given below:
enter image source here
Hope it helps.
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