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19.11.2020 •
Mathematics
What is the slope of the line
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Ответ:
For this problem we have 3 options.
1) We can use the completing the square the method to put the equations in Standard Vertex Form,
(
x
−
h
)
2
−
k
=
0
→
v
e
r
t
e
x
(
h
,
−
k
)
2) We can use the expression
(
−
b
2
a
,
f
(
−
b
2
a
)
)
where
a
and
b
are the coefficients found when the equation is in standard form,
a
x
2
+
b
x
+
c
=
0
3) We could just graph it.
Let do options 1 & 2.
Completing the Square:
x
2
−
2
x
−
1
=
0
x
2
−
2
x
=
1
(
−
2
2
)
2
=
(
−
1
)
2
=
1
, We will add
1
to both sides of the equation.
x
2
−
2
x
+
1
=
1
+
1
x
2
−
2
x
+
1
=
2
(
x
−
1
)
2
=
2
(
x
−
1
)
2
−
2
=
0
→
v
e
r
t
e
x
→
(
1
,
−
2
)
Solution
(
x
−
h
)
2
−
k
=
0
→
v
e
r
t
e
x
→
(
h
,
−
k
)
Using the expression
(
−
b
2
a
,
f
(
−
b
2
a
)
)
:
a
=
1
,
b
=
−
2
,
c
=
−
1
x
=
−
b
2
a
=
−
−
2
2
(
1
)
=
2
2
(
1
)
=
2
2
=
1
y
=
f
(
−
b
2
a
)
=
f
(
1
)
=
(
1
)
2
−
2
(
1
)
−
1
=
1
−
2
−
1
=
−
2
v
e
r
t
e
x
→
(
1
,
−
2
)
Solution
Notice that both methods produced the same results.