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Let’s check out your problem:
1
1
1
). Vertex at origin, Focus:
(
0
,
1
4
)
\left(0, \frac{1}{4}\right)
(
0
,
4
1
)
\newline
A)
y
=
x
2
y=x^{2}
y
=
x
2
\newline
B)
y
=
4
x
2
y=4 x^{2}
y
=
4
x
2
\newline
C)
y
=
−
(
x
+
2
)
2
−
1
y=-(x+2)^{2}-1
y
=
−
(
x
+
2
)
2
−
1
\newline
D)
y
=
−
(
x
+
2
)
2
+
1
y=-(x+2)^{2}+1
y
=
−
(
x
+
2
)
2
+
1
\newline
E)
y
=
−
x
2
y=-x^{2}
y
=
−
x
2
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Math Problems
Geometry
Write equations of parabolas in vertex form using the focus and directrix
Full solution
Q.
1
1
1
). Vertex at origin, Focus:
(
0
,
1
4
)
\left(0, \frac{1}{4}\right)
(
0
,
4
1
)
\newline
A)
y
=
x
2
y=x^{2}
y
=
x
2
\newline
B)
y
=
4
x
2
y=4 x^{2}
y
=
4
x
2
\newline
C)
y
=
−
(
x
+
2
)
2
−
1
y=-(x+2)^{2}-1
y
=
−
(
x
+
2
)
2
−
1
\newline
D)
y
=
−
(
x
+
2
)
2
+
1
y=-(x+2)^{2}+1
y
=
−
(
x
+
2
)
2
+
1
\newline
E)
y
=
−
x
2
y=-x^{2}
y
=
−
x
2
Identify Parabola Orientation:
Since the vertex is at the origin
(
0
,
0
)
(0,0)
(
0
,
0
)
and the focus is at
(
0
,
1
4
)
(0,\frac{1}{4})
(
0
,
4
1
)
, the parabola is vertical.
Calculate Distance to Focus:
The distance from the vertex to the focus,
p
p
p
, is
1
4
\frac{1}{4}
4
1
.
Use Standard Form Equation:
The standard form of a vertical parabola is
y
=
4
p
x
2
y = 4px^2
y
=
4
p
x
2
.
Substitute
p
p
p
Value:
Substitute
p
=
1
4
p = \frac{1}{4}
p
=
4
1
into the standard form equation to get
y
=
4
(
1
4
)
x
2
y = 4\left(\frac{1}{4}\right)x^2
y
=
4
(
4
1
)
x
2
.
Simplify Equation:
Simplify the equation to
y
=
x
2
y = x^2
y
=
x
2
.
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y - 8x^2 = 4
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?
\newline
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(
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(ด้) BEATRICE MAYES INSTITUTE CHARTER SCHOOL
\newline
4
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\newline
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\newline
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\newline
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\newline
Clear
\newline
Adam's Expenses
\newline
\begin{tabular}{|c|c|c|}
\newline
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\newline
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25.00
\$ 25.00
$25.00
&
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\$ 25.00
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\$ 25.00
$25.00
&
$
20.00
\$ 20.00
$20.00
\\
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\end{tabular}
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\newline
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\newline
(B) Both school lunches and book fairs are fixed expenses.
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(C) Both school lunches and book fairs are variable expenses.
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Which of the following is a whole number?
\newline
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\newline
(A)
0
0
0
\newline
(B)
5
\sqrt{5}
5
\newline
(C)
π
\pi
π
\newline
(D)
−
9
-9
−
9
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Question
Which of the following is a natural number?
\newline
Choices:
\newline
(A)
π
\pi
π
\newline
(B)
−
2
-2
−
2
\newline
(C)
5
5
5
\newline
(D)
7
\sqrt{7}
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Evaluate
x
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x
.
\newline
(
x
4
7
−
8
)
−
7
\left(\dfrac{x^{4}}{7^{-8}}\right)^{-7}
(
7
−
8
x
4
)
−
7
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y= -x^2
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?
\newline
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Use the distributive property to multiply.
\newline
(
2
x
+
5
)
(
x
2
+
2
x
−
4
)
(2 x+5)\left(x^{2}+2 x-4\right)
(
2
x
+
5
)
(
x
2
+
2
x
−
4
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Question
What is the sum of
12
x
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1
,
9
x
+
1
12 x+1,9 x+1
12
x
+
1
,
9
x
+
1
, and
6
x
+
1
6 x+1
6
x
+
1
?
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9
x
+
1
9 x+1
9
x
+
1
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27
x
+
3
27 x+3
27
x
+
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x
+
1
15 x+1
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x
+
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18
x
+
3
18 x+3
18
x
+
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2
2
2
. Find the sum of all the factors of
16
16
16
.
\newline
(
1
1
1
)
30
30
30
\newline
(
2
2
2
)
31
31
31
\newline
(
3
3
3
)
34
34
34
\newline
(
4
4
4
)
35
35
35
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