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Algebra 2
Write equations of parabolas in vertex form using properties
label the vertex, focus, and directrix of the equation of the parabola
\newline
y
=
−
3
(
x
−
4
)
2
+
1
y = -3(x-4)^2 + 1
y
=
−
3
(
x
−
4
)
2
+
1
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and focus
(
0
,
3
)
(0,3)
(
0
,
3
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
3
)
(0,-3)
(
0
,
−
3
)
and focus
(
0
,
4
)
(0,4)
(
0
,
4
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
and directrix
y
=
−
4
y = -4
y
=
−
4
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
8
)
(0,8)
(
0
,
8
)
and focus
(
0
,
7
)
(0,7)
(
0
,
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
−
3
y = -3
y
=
−
3
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
1
)
(0,-1)
(
0
,
−
1
)
and focus
(
0
,
4
)
(0,4)
(
0
,
4
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
4
)
(0,4)
(
0
,
4
)
and focus
(
0
,
0
)
(0,0)
(
0
,
0
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
6
)
(0,-6)
(
0
,
−
6
)
and directrix
y
=
−
7
y = -7
y
=
−
7
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
6
)
(0,-6)
(
0
,
−
6
)
and directrix
y
=
−
2
y = -2
y
=
−
2
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and directrix
y
=
−
9
y = -9
y
=
−
9
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and focus
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
8
y = 8
y
=
8
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and directrix
y
=
6
y = 6
y
=
6
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
4
)
(0,4)
(
0
,
4
)
and focus
(
0
,
2
)
(0,2)
(
0
,
2
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
7
)
(0,7)
(
0
,
7
)
and focus
(
0
,
10
)
(0,10)
(
0
,
10
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
−
10
y = -10
y
=
−
10
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
3
y = 3
y
=
3
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
3
)
(0,-3)
(
0
,
−
3
)
and focus
(
0
,
−
1
)
(0,-1)
(
0
,
−
1
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
8
)
(0,8)
(
0
,
8
)
and focus
(
0
,
9
)
(0,9)
(
0
,
9
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
8
)
(0,-8)
(
0
,
−
8
)
and focus
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
4
)
(0,4)
(
0
,
4
)
and focus
(
0
,
7
)
(0,7)
(
0
,
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
5
)
(0,5)
(
0
,
5
)
and focus
(
0
,
7
)
(0,7)
(
0
,
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
7
)
(0,7)
(
0
,
7
)
and directrix
y
=
6
y = 6
y
=
6
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
1
)
(0,1)
(
0
,
1
)
and focus
(
0
,
3
)
(0,3)
(
0
,
3
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
2
)
(0,2)
(
0
,
2
)
and directrix
y
=
5
y = 5
y
=
5
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
and directrix
y
=
−
5
y = -5
y
=
−
5
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and focus
(
0
,
6
)
(0,6)
(
0
,
6
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and focus
(
0
,
−
8
)
(0,-8)
(
0
,
−
8
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and focus
(
0
,
9
)
(0,9)
(
0
,
9
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
5
)
(0,-5)
(
0
,
−
5
)
and focus
(
0
,
0
)
(0,0)
(
0
,
0
)
.
\newline
Simplify any fractions.
\newline
______
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The side length of a square is decreasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side length is
9
9
9
kilometers.
\newline
What is the rate of change of the area of the square at that instant (in square kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
81
-81
−
81
\newline
(B)
−
36
-36
−
36
\newline
(C)
−
4
-4
−
4
\newline
(D)
−
324
-324
−
324
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Find the
a
a
a
value of a parabola that has a vertex at
(
−
3
,
−
4
)
(-3,-4)
(
−
3
,
−
4
)
and the point
(
−
6
,
−
25
4
)
(-6,-\frac{25}{4})
(
−
6
,
−
4
25
)
that lies on the curve.
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1
1
1
. Find the values of
x
x
x
and
y
y
y
such that the number
56129137
X
51
Y
56129137 \mathrm{X} 51 \mathrm{Y}
56129137
X
51
Y
is divisible by
88
88
88
\newline
(a)
2
2
2
,
2
2
2
\newline
(b)
4
4
4
,
2
2
2
\newline
(c)
4
4
4
,
4
4
4
\newline
(d) none of these
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Write the equation in vertex form for the parabola with focus
(
7
,
15
4
)
\left(7, \frac{15}{4}\right)
(
7
,
4
15
)
and directrix
y
=
−
15
4
y=-\frac{15}{4}
y
=
−
4
15
.
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Determine the equation of the parabola with vertex
(
−
8
,
5
)
(-8,5)
(
−
8
,
5
)
and directrix
y
=
−
3
y=-3
y
=
−
3
.
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