Answer:
Step-by-step explanation:
f
(
x
)
=
−
4
(
x
−
8
)
2
+
3
Set the polynomial equal to
y
to find the properties of the parabola.
y
=
−
4
(
x
−
8
)
2
+
3
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
−
4
h
=
8
k
=
3
Since the value of
a
is negative, the parabola opens down.
Opens Down
Find the vertex
(
h
,
k
)
.
(
8
,
3
)
Find
p
, the distance from the vertex to the focus.
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−
1
16
Find the focus.
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(
8
,
47
16
)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x
=
8
image of graph
Answer:
f(x) = (-1/2)(x^2 + 8x - 15)
Step-by-step explanation:
This function has two roots: -3 and 5. Most likely it is a quadratic (all of which have two roots).
Then f(x) = a(x + 3)(x - 5)
The graph goes through (1. 8): Therefore, y = 8 when x = 1:
f(1) = a(1 + 3)(1 - 5) = 8, or
a(4)(-4) = 8, or
-16a = 8, which leads to a = -1/2.
Thus the quadratic in question is f(x) = (-1/2)(x + 3)(x - 5), or
f(x) = (-1/2)(x^2 + 8x - 15)
Answer:
6 2/7
Step-by-step explanation:
