How to find the parabola with maximum value 8 at x= -1, and passing through point (-3, 5)?
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0
Answer:
The equation is
y
=
3
x
2
−
2
x
+
7
Explanation:
The slope at a point is
=
the derivative.
Let
f
(
x
)
=
a
x
2
+
b
x
+
c
f
'
(
x
)
=
2
a
x
+
b
f
'
(
1
)
=
2
a
+
b
=
4
, this is equation
1
and
f
'
(
−
1
)
=
−
2
a
+
b
=
−
8
, this is equation
2
Adding the 2 equations, we get
2
b
=
−
4
,
⇒
,
b
=
−
2
2
a
−
2
=
4
, from equation
1
a
=
3
Therefore,
f
(
x
)
=
3
x
2
−
2
x
+
c
The parabola passes through
(
2
,
15
)
So,
f
(
2
)
=
3
⋅
4
−
2
⋅
2
+
c
=
8
+
c
=
15
c
=
15
−
8
=
7
Finally
f
(
x
)
=
3
x
2
−
2
x
+
7
Step-by-step explanation:
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