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Math Problems
Algebra 2
Write a quadratic function in vertex form
question: \begin{aligned} &f(c)=
3
3
3
c
−
8
-8
−
8
\ &g(c)=\sqrt{
14
14
14
-c} \end{aligned}
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Solve the inequality and graph the solution.
\newline
2.5
m
−
1.5
(
2
−
3
m
)
>
2
(
m
+
1
)
2.5m - 1.5(2 - 3m) > 2(m + 1)
2.5
m
−
1.5
(
2
−
3
m
)
>
2
(
m
+
1
)
\newline
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.
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Consider the polynomial function
g
(
x
)
=
10
x
9
−
50
x
6
−
500
x
2
g(x) = 10x^9 - 50x^6 - 500x^2
g
(
x
)
=
10
x
9
−
50
x
6
−
500
x
2
. What is the end behavior of the graph of
g
g
g
?
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The parabola
y
=
x
2
y=x^2
y
=
x
2
is scaled vertically by a factor of
1
10
\frac{1}{10}
10
1
. What is the equation of the new parabola?
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The graph of the function
y
=
x
2
y=x^{2}
y
=
x
2
is shown. How will the graph change if the equation is changed to
y
=
(
1
/
4
)
x
2
y=(1 / 4) x^{2}
y
=
(
1/4
)
x
2
?
\newline
The parabola will become narrower.
\newline
The parabola will move up
1
/
4
1 / 4
1/4
unit.
\newline
The parabola will become wider.
\newline
The parabola will move down
1
/
4
1 / 4
1/4
unit.
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Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
−
6
x
−
7
y=x^{2}-6 x-7
y
=
x
2
−
6
x
−
7
\newline
Answer:
y
=
y=
y
=
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Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
+
2
x
−
7
y=x^{2}+2 x-7
y
=
x
2
+
2
x
−
7
\newline
Answer:
y
=
y=
y
=
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A parabola graphed in the
x
y
x y
x
y
-plane has equation
y
=
2
x
2
−
5
x
−
3
y=2 x^{2}-5 x-3
y
=
2
x
2
−
5
x
−
3
. What is the
x
x
x
-coordinate of the vertex of the parabola?
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A parabola graphed in the
x
y
x y
x
y
-plane has equation
y
=
−
3
x
2
+
9
x
−
2
y=-3 x^{2}+9 x-2
y
=
−
3
x
2
+
9
x
−
2
. What is the
y
y
y
-coordinate of the vertex of the parabola?
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The equation of a parabola is
y
=
5
x
2
+
20
x
+
18
y = 5x^2 + 20x + 18
y
=
5
x
2
+
20
x
+
18
. Write the equation in vertex form.
\newline
Write any numbers as integers or simplified proper or improper fractions.
\newline
______
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