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Math Problems
Algebra 2
Convert equations of parabolas from general to vertex form
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
□
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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
______
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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
______
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
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
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If
y
=
1
3
(
x
−
2
)
2
y=\frac{1}{3}(x-2)^2
y
=
3
1
(
x
−
2
)
2
is graphed in the
x
y
xy
x
y
-plane, which of the following characteristics of the graph are displayed as a constant or coefficient in the equation?
\newline
-
y
y
y
-intercept(s)
\newline
-
x
x
x
-intercept
\newline
-
y
y
y
-coordinate of the line of symmetry
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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 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
−
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
−
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
+
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
+
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
−
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
−
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
+
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)
(
□
,
□
)
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
+
8
x
−
9
y=x^{2}+8 x-9
y
=
x
2
+
8
x
−
9
\newline
Answer:
y
=
y=
y
=
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
+
8
x
+
9
y=x^{2}+8 x+9
y
=
x
2
+
8
x
+
9
\newline
Answer:
y
=
y=
y
=
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
−
6
x
+
8
y=x^{2}-6 x+8
y
=
x
2
−
6
x
+
8
\newline
Answer:
y
=
y=
y
=
Get tutor help
The function
\newline
f
f
f
is given in three equivalent forms.
\newline
Which form most quickly reveals the vertex?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
x
)
=
−
3
(
x
−
2
)
2
+
27
f(x)=-3(x-2)^{2}+27
f
(
x
)
=
−
3
(
x
−
2
)
2
+
27
\newline
(B)
f
(
x
)
=
−
3
(
x
+
1
)
(
x
−
5
)
f(x)=-3(x+1)(x-5)
f
(
x
)
=
−
3
(
x
+
1
)
(
x
−
5
)
\newline
(C)
f
(
x
)
=
−
3
x
2
+
12
x
+
15
f(x)=-3x^{2}+12x+15
f
(
x
)
=
−
3
x
2
+
12
x
+
15
\newline
What is the vertex?
\newline
Vertex
=
(
□
,
□
)
=(\square,\square)
=
(
□
,
□
)
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