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Let’s check out your problem:
Write the standard form of
y
=
5
(
x
−
8
)
2
+
4
y=5(x-8)^{2}+4
y
=
5
(
x
−
8
)
2
+
4
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Math Problems
Algebra 1
Write a quadratic function from its x-intercepts and another point
Full solution
Q.
Write the standard form of
y
=
5
(
x
−
8
)
2
+
4
y=5(x-8)^{2}+4
y
=
5
(
x
−
8
)
2
+
4
Expand squared term:
Expand the squared term in the equation.
\newline
Calculation:
(
x
−
8
)
2
=
x
2
−
16
x
+
64
(x - 8)^2 = x^2 - 16x + 64
(
x
−
8
)
2
=
x
2
−
16
x
+
64
.
\newline
y =
5
(
x
2
−
16
x
+
64
)
+
4
5(x^2 - 16x + 64) + 4
5
(
x
2
−
16
x
+
64
)
+
4
.
Distribute
5
5
5
:
Distribute the
5
5
5
across the terms inside the parentheses.
\newline
Calculation:
y
=
5
x
2
−
80
x
+
320
+
4
y = 5x^2 - 80x + 320 + 4
y
=
5
x
2
−
80
x
+
320
+
4
.
Combine like terms:
Combine like terms.
\newline
Calculation:
y
=
5
x
2
−
80
x
+
324
y = 5x^2 - 80x + 324
y
=
5
x
2
−
80
x
+
324
.
More problems from Write a quadratic function from its x-intercepts and another point
Question
The function
h
h
h
is defined over the real numbers. This table gives a few values of
h
h
h
.
\newline
\begin{tabular}{lllll}
\newline
x
x
x
&
−
6
-6
−
6
.
1
1
1
&
−
6
-6
−
6
.
01
01
01
&
−
6
-6
−
6
.
001
001
001
&
−
5
-5
−
5
.
9
9
9
\\
\newline
\hline
h
(
x
)
h(x)
h
(
x
)
&
−
0
-0
−
0
.
25
25
25
&
−
0
-0
−
0
.
74
74
74
&
−
0
-0
−
0
.
98
98
98
&
−
1
-1
−
1
.
0
0
0
\newline
\end{tabular}
\newline
What is a reasonable estimate for
lim
x
→
−
6
h
(
x
)
\lim _{x \rightarrow-6} h(x)
lim
x
→
−
6
h
(
x
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
-6
−
6
\newline
(B)
−
2
-2
−
2
\newline
(C)
−
1
-1
−
1
\newline
(D) The limit doesn't exist
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Posted 4 months ago
Question
What is the amplitude of
\newline
g
(
x
)
=
−
2
sin
(
π
2
x
−
3
)
+
5
?
g(x)=-2 \sin \left(\frac{\pi}{2} x-3\right)+5 ?
g
(
x
)
=
−
2
sin
(
2
π
x
−
3
)
+
5
?
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the amplitude of
y
=
5
sin
(
4
x
−
2
)
−
3
y=5 \sin (4 x-2)-3
y
=
5
sin
(
4
x
−
2
)
−
3
?
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the amplitude of
y
=
−
3
cos
(
π
x
+
2
)
−
6
?
y=-3 \cos (\pi x+2)-6 ?
y
=
−
3
cos
(
π
x
+
2
)
−
6
?
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the amplitude of
y
=
3
sin
(
2
x
−
1
)
+
4
y=3 \sin (2 x-1)+4
y
=
3
sin
(
2
x
−
1
)
+
4
?
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the period of the function
h
(
x
)
=
−
3
cos
(
π
x
+
2
)
−
6
?
h(x)=-3 \cos (\pi x+2)-6 ?
h
(
x
)
=
−
3
cos
(
π
x
+
2
)
−
6
?
\newline
Give an exact value.
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the period of the function
\newline
h
(
x
)
=
5
sin
(
4
x
−
2
)
−
3
?
h(x)=5 \sin (4 x-2)-3 \text { ? }
h
(
x
)
=
5
sin
(
4
x
−
2
)
−
3
?
\newline
Give an exact value.
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the period of the function
g
(
x
)
=
2
cos
(
7
x
+
5
)
+
1
?
g(x)=2 \cos (7 x+5)+1 ?
g
(
x
)
=
2
cos
(
7
x
+
5
)
+
1
?
\newline
Give an exact value.
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the period of the function
f
(
x
)
=
3
sin
(
2
x
−
1
)
+
4
f(x)=3 \sin (2 x-1)+4
f
(
x
)
=
3
sin
(
2
x
−
1
)
+
4
?
\newline
Give an exact value.
\newline
units
Get tutor help
Posted 3 months ago
Question
What is the period of the function
f
(
x
)
=
−
4
cos
(
5
x
−
9
)
−
7
f(x)=-4 \cos (5 x-9)-7
f
(
x
)
=
−
4
cos
(
5
x
−
9
)
−
7
?
\newline
Give an exact value.
\newline
units
Get tutor help
Posted 3 months ago