Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Write a quadratic function in vertex form
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
?
Get tutor help
The diagram shows the curve
y
=
x
2
−
3
x
+
1
y=x^{2}-3 x+1
y
=
x
2
−
3
x
+
1
and the line
y
=
5
y=5
y
=
5
.
\newline
Find the area of the shaded region. Give your answer as a fraction in its simplest form.
Get tutor help
\begin{tabular}{|l|l|}
\newline
\hline You get this: & Fill in this: \\
\newline
\hline
y
=
−
x
2
−
6
x
+
16
y=-x^{2}-6 x+16
y
=
−
x
2
−
6
x
+
16
& Either form of the equation other than standard form: \\
\newline
\cline {
1
1
1
-
2
2
2
} & Vertex of the parabola: \\
\newline
\cline {
2
2
2
-
2
2
2
} &
x
x
x
-intercepts and
y
y
y
-intercept: \\
\newline
\hline
\newline
\end{tabular}
Get tutor help
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?
Get tutor help
y
=
x
2
−
6
x
+
6
y=x^2-6x+6
y
=
x
2
−
6
x
+
6
Which of the following is an equivalent form of the equation of the graph shown in the
x
y
xy
x
y
-plane, from which the coordinates of vertex
V
V
V
can be identified as constants in the equation?
Get tutor help
The graph of the function
\newline
y
=
x
2
y=x^{2}
y
=
x
2
is shown. How will the graph change if the equation is changed to
\newline
y
=
(
1
4
)
x
2
y=\left(\frac{1}{4}\right)x^{2}
y
=
(
4
1
)
x
2
?
\newline
The parabola will become narrower.
\newline
The parabola will move up
1
4
\frac{1}{4}
4
1
unit.
\newline
The parabola will become wider.
\newline
The parabola will move down
\newline
1
4
\frac{1}{4}
4
1
unit.
Get tutor help
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.
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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?
Get tutor help
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?
Get tutor help
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
______
Get tutor help
