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Math Problems
Algebra 2
Convert equations of parabolas from general to vertex form
Graph the function
f
(
x
)
=
−
6
x
2
f(x)=-6 x^{2}
f
(
x
)
=
−
6
x
2
.
\newline
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.
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Consider the following quadratic function.
\newline
f
(
x
)
=
−
2
x
2
−
8
x
−
13
f(x)=-2 x^{2}-8 x-13
f
(
x
)
=
−
2
x
2
−
8
x
−
13
\newline
(a) Write the equation in the form
f
(
x
)
=
a
(
x
−
h
)
2
+
k
f(x)=a(x-h)^{2}+k
f
(
x
)
=
a
(
x
−
h
)
2
+
k
. Then give the vertex of its graph.
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Consider the following quadratic function.
\newline
f
(
x
)
=
−
3
x
2
+
6
x
−
1
f(x)=-3 x^{2}+6 x-1
f
(
x
)
=
−
3
x
2
+
6
x
−
1
\newline
(a) Write the equation in the form
f
(
x
)
=
a
(
x
−
h
)
2
+
k
f(x)=a(x-h)^{2}+k
f
(
x
)
=
a
(
x
−
h
)
2
+
k
. Then give the vertex of its graph.
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Graph the function
f
(
x
)
=
4
x
2
+
8
x
−
1
f(x)=4 x^{2}+8 x-1
f
(
x
)
=
4
x
2
+
8
x
−
1
\newline
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.
Get tutor help
Graph the function
f
(
x
)
=
x
2
+
4
x
+
5
f(x)=x^{2}+4 x+5
f
(
x
)
=
x
2
+
4
x
+
5
.
\newline
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.
\newline
Time
\newline
elapsed
\newline
PAUSED
\newline
SmartScore
\newline
out of
100
100
100
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y
=
2
x
2
−
6
x
−
5
y=2 x^{2}-6 x-5
y
=
2
x
2
−
6
x
−
5
(Use decimals in your answers.)
\newline
Axis of symmetry:
□
\square
□
\newline
Vertex:
□
\square
□
Get tutor help
39
39
39
. The graph of
g
(
x
)
=
−
3
(
x
−
4
)
2
+
5
g(x)=-3(x-4)^{2}+5
g
(
x
)
=
−
3
(
x
−
4
)
2
+
5
is translated
6
6
6
units left and
9
9
9
units down. What is the value of
h
h
h
when the equation of the transformed graph is written in vertex form?
\newline
(A)
−
4
-4
−
4
\newline
(B)
−
2
-2
−
2
\newline
(C)
2
2
2
\newline
(D)
10
10
10
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The equation of a parabola is
y
=
x
2
−
6
x
+
17
y = x^2 - 6x + 17
y
=
x
2
−
6
x
+
17
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
−
6
x
+
18
y = x^2 - 6x + 18
y
=
x
2
−
6
x
+
18
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
−
10
x
+
19
y = x^2 - 10x + 19
y
=
x
2
−
10
x
+
19
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
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Use the figure to complete each part.
\newline
(a) Write two other names for
∠
R
Q
S
\angle R Q S
∠
RQS
.
R
S
Q
R S Q
RSQ
and
S
Q
R
S Q R
SQR
\newline
(b) Name the vertex of
∠
S
Q
T
\angle S Q T
∠
SQT
.
\newline
T
\newline
(c) Name the sides of
∠
1
\angle 1
∠1
.
\newline
□
\square
□
and
□
\square
□
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Which equation is
y
=
9
x
2
+
9
x
−
1
y=9 x^{2}+9 x-1
y
=
9
x
2
+
9
x
−
1
rewritten in vertex form?
\newline
y
=
9
(
x
+
1
2
)
2
−
13
4
y=9\left(x+\frac{1}{2}\right)^{2}-\frac{13}{4}
y
=
9
(
x
+
2
1
)
2
−
4
13
\newline
y
=
9
(
x
+
1
2
)
2
−
1
y=9\left(x+\frac{1}{2}\right)^{2}-1
y
=
9
(
x
+
2
1
)
2
−
1
\newline
y
=
9
(
x
+
1
2
)
2
+
5
4
y=9\left(x+\frac{1}{2}\right)^{2}+\frac{5}{4}
y
=
9
(
x
+
2
1
)
2
+
4
5
\newline
y
=
9
(
x
+
1
2
)
2
−
5
4
y=9\left(x+\frac{1}{2}\right)^{2}-\frac{5}{4}
y
=
9
(
x
+
2
1
)
2
−
4
5
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Graph the function
f
(
x
)
=
4
x
2
f(x)=4 x^{2}
f
(
x
)
=
4
x
2
.
\newline
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you c erase your parabola by selecting the second point and placing it on top of the first.
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Find the inverse
f
(
x
)
=
x
2
+
8
,
x
>
0
f(x)=x^2+8, x>0
f
(
x
)
=
x
2
+
8
,
x
>
0
Get tutor help
The equation of a parabola is
y
=
x
2
+
8
x
+
18
y = x^2 + 8x + 18
y
=
x
2
+
8
x
+
18
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
−
8
x
+
18
y = x^2 - 8x + 18
y
=
x
2
−
8
x
+
18
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
+
10
x
+
18
y = x^2 + 10x + 18
y
=
x
2
+
10
x
+
18
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
+
6
x
+
18
y = x^2 + 6x + 18
y
=
x
2
+
6
x
+
18
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
−
8
x
+
17
y = x^2 - 8x + 17
y
=
x
2
−
8
x
+
17
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
−
6
x
+
19
y = x^2 - 6x + 19
y
=
x
2
−
6
x
+
19
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
The equation of a parabola is
y
=
x
2
+
6
x
+
19
y = x^2 + 6x + 19
y
=
x
2
+
6
x
+
19
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
Get tutor help
Simplify. Write your answer using whole numbers and variables.
\newline
9
x
2
+
2
x
9
x
+
2
\frac{9x^2 + 2x}{9x + 2}
9
x
+
2
9
x
2
+
2
x
Get tutor help
F
(
x
)
=
3
x
2
−
16
+
21
F(x)=3x^2-16+21
F
(
x
)
=
3
x
2
−
16
+
21
find the zeros of the functions
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F
(
x
)
=
3
x
2
−
16
+
21
F(x)=3x^2-16+21
F
(
x
)
=
3
x
2
−
16
+
21
find the zeros of the function
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
4
x
+
29
y=x^{2}+4 x+29
y
=
x
2
+
4
x
+
29
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
2
x
+
13
y=x^{2}+2 x+13
y
=
x
2
+
2
x
+
13
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
12
x
+
20
y=x^{2}-12 x+20
y
=
x
2
−
12
x
+
20
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
2
x
+
37
y=x^{2}+2 x+37
y
=
x
2
+
2
x
+
37
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
16
x
y=x^{2}-16 x
y
=
x
2
−
16
x
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
8
x
+
41
y=x^{2}-8 x+41
y
=
x
2
−
8
x
+
41
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
14
x
+
24
y=x^{2}+14 x+24
y
=
x
2
+
14
x
+
24
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
4
x
−
12
y=x^{2}-4 x-12
y
=
x
2
−
4
x
−
12
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
10
x
−
2
y=x^{2}+10 x-2
y
=
x
2
+
10
x
−
2
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
12
x
+
32
y=x^{2}-12 x+32
y
=
x
2
−
12
x
+
32
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
8
x
−
2
y=x^{2}-8 x-2
y
=
x
2
−
8
x
−
2
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
12
x
−
13
y=x^{2}-12 x-13
y
=
x
2
−
12
x
−
13
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
2
x
+
37
y=x^{2}+2 x+37
y
=
x
2
+
2
x
+
37
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
\newline
Submit Answer
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
10
x
+
50
y=x^{2}-10 x+50
y
=
x
2
−
10
x
+
50
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
2
x
−
24
y=x^{2}+2 x-24
y
=
x
2
+
2
x
−
24
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
4
x
−
21
y=x^{2}+4 x-21
y
=
x
2
+
4
x
−
21
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
8
x
−
16
y=x^{2}+8 x-16
y
=
x
2
+
8
x
−
16
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
2
x
−
35
y=x^{2}-2 x-35
y
=
x
2
−
2
x
−
35
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
14
x
+
22
y=x^{2}+14 x+22
y
=
x
2
+
14
x
+
22
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
10
x
+
16
y=x^{2}+10 x+16
y
=
x
2
+
10
x
+
16
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
4
x
−
32
y=x^{2}-4 x-32
y
=
x
2
−
4
x
−
32
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
4
x
+
5
y=x^{2}+4 x+5
y
=
x
2
+
4
x
+
5
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
10
x
+
9
y=x^{2}+10 x+9
y
=
x
2
+
10
x
+
9
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
10
x
+
24
y=x^{2}+10 x+24
y
=
x
2
+
10
x
+
24
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
−
20
x
+
25
y=x^{2}-20 x+25
y
=
x
2
−
20
x
+
25
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Put the quadratic into vertex form and state the coordinates of the vertex.
\newline
y
=
x
2
+
2
x
+
3
y=x^{2}+2 x+3
y
=
x
2
+
2
x
+
3
\newline
Vertex Form:
y
=
y=
y
=
\newline
Vertex:
(
□
,
□
)
(\square, \square)
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