Step-by-step explanation:
What is the equation of the parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
?
To solve this you need to use the vertex form of the equation of a parabola which is
y
=
a
(
x
−
h
)
2
+
k
, where
(
h
,
k
)
are the coordinates of the vertex.
Explanation:
The first step is to define your variables
h
=
−
4
k
=
2
And we know one set of points on the graph, so
x
=
−
7
y
=
−
34
Next solve the formula for
a
y
=
a
(
x
−
h
)
2
+
k
−
34
=
a
(
−
7
+
4
)
2
+
2
−
34
=
a
(
−
3
)
2
+
2
−
34
=
9
a
+
2
−
36
=
9
a
−
4
=
a
To create a general formula for the parabola you would put in the values for
a
,
h
, and
k
and then simplify.
y
=
a
(
x
−
h
)
2
+
k
y
=
−
4
(
x
+
4
)
2
+
2
y
=
−
4
(
x
2
+
8
x
+
16
)
+
2
y
=
−
4
x
2
−
32
x
−
64
+
2
So the equation of a parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
is:
y
=
−
4
x
2
−
32
x
−
62
Answer: They can do 56 different combinations.
Step-by-step explanation:
Step-by-step explanation:
f(g(x))=(3x+1)^2 +2(3x+1) -4
=9x^2 +6x +1 +6x +2 -4
=9x^2 +12x +(-1)
Answer:
V = 3591.4 ft³
Step-by-step explanation:
The formula for the volume of a sphere whose radius is given is
V = (4/3)πr³
Here we have V = (4/3)(3.14)(9.5 ft)³, or:
V = 3591.4 ft³
