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Math Problems
Algebra 1
Write a quadratic function from its x-intercepts and another point
In the
x
y
x y
x
y
-plane, the graph of a quadratic function has
x
x
x
-intercepts at
(
−
3
,
0
)
(-3,0)
(
−
3
,
0
)
and
(
7
,
0
)
(7,0)
(
7
,
0
)
. If the parabola has an axis of symmetry of
x
=
h
x=h
x
=
h
, then what is the value of
h
h
h
?
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In the
x
y
x y
x
y
-plane, the graph of the equation
y
=
3
(
x
+
6
)
2
+
5
y=3(x+6)^{2}+5
y
=
3
(
x
+
6
)
2
+
5
has a
y
y
y
-intercept of
(
0
,
b
)
(0, b)
(
0
,
b
)
. What is the value of
b
b
b
?
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The equation
y
=
30
(
1
2
)
x
y=30\left(\frac{1}{2}\right)^{x}
y
=
30
(
2
1
)
x
is graphed in the
x
y
x y
x
y
-plane. Which of the following statements about the graph is true?
\newline
Choose
1
1
1
answer:
\newline
(A) As
x
x
x
increases,
y
y
y
increases at an increasing rate.
\newline
(B) As
x
x
x
increases,
y
y
y
increases at a decreasing rate.
\newline
(C) As
x
x
x
increases,
y
y
y
decreases at an increasing rate.
\newline
(D) As
x
x
x
increases,
y
y
y
decreases at a decreasing rate.
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The equation
5
x
+
10
y
=
30
5 x+10 y=30
5
x
+
10
y
=
30
is graphed in the
x
y
x y
x
y
-plane. Which of the statements below is true of its graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph's
x
x
x
-intercept is
3
3
3
and its
y
y
y
-intercept is
6
6
6
.
\newline
(B) The graph has a slope of
1
2
\frac{1}{2}
2
1
.
\newline
(C) The graph has a slope of
−
2
1
-\frac{2}{1}
−
1
2
.
\newline
D The graph's
x
x
x
-intercept is
6
6
6
and its
y
y
y
-intercept is
3
3
3
.
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A line is graphed in the
x
y
x y
x
y
-plane shown. Which of the following is an equation of the line, if the line passes through the points
(
0
,
0
)
(0, 0)
(
0
,
0
)
and
(
2
,
−
3
)
(2, -3)
(
2
,
−
3
)
?
?
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
3
2
x
y=\frac{3}{2} x
y
=
2
3
x
\newline
(B)
y
=
2
3
x
y=\frac{2}{3} x
y
=
3
2
x
\newline
(C)
y
=
−
3
2
x
y=-\frac{3}{2} x
y
=
−
2
3
x
\newline
(D)
y
=
−
2
3
x
y=-\frac{2}{3} x
y
=
−
3
2
x
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The equation
2
x
−
y
=
8
2 x-y=8
2
x
−
y
=
8
is graphed in the
x
y
x y
x
y
-plane. Which of the following is a true statement about the graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph's
x
x
x
-intercept is
4
4
4
and its
y
y
y
-intercept is
−
8
-8
−
8
.
\newline
B The graph's
x
x
x
-intercept is
4
4
4
and its
y
y
y
-intercept is
8
8
8
.
\newline
(C) The graph has a slope of
−
2
-2
−
2
.
\newline
D The graph has a slope of
1
2
\frac{1}{2}
2
1
.
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The equation
6
−
2
y
=
x
6-2 y=x
6
−
2
y
=
x
is graphed in the
x
y
x y
x
y
-plane. Which of the following is a true statement about the graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph's
x
x
x
-intercept is
6
6
6
and its
y
y
y
-intercept is
−
2
-2
−
2
.
\newline
B The graph's
x
x
x
-intercept is
6
6
6
and its
y
y
y
-intercept is
2
2
2
.
\newline
(C) The graph has a slope of
−
2
-2
−
2
.
\newline
D) The graph has a slope of
−
1
2
-\frac{1}{2}
−
2
1
.
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The equation
6
y
−
3
x
=
5
6 y-3 x=5
6
y
−
3
x
=
5
is graphed in the
x
y
x y
x
y
-plane. Which of the following is a true statement about the graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph's
x
x
x
-intercept is
5
6
\frac{5}{6}
6
5
and its
y
y
y
-intercept is
−
5
3
-\frac{5}{3}
−
3
5
.
\newline
(B) The graph's
x
x
x
-intercept is
−
5
3
-\frac{5}{3}
−
3
5
and its
y
y
y
-intercept is
5
6
\frac{5}{6}
6
5
.
\newline
(C) The graph has a slope of
2
2
2
.
\newline
D The graph has a slope of
−
1
2
-\frac{1}{2}
−
2
1
.
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The line represented by the equation
3.4
y
=
0
3.4 y=0
3.4
y
=
0
is graphed in the
x
y
x y
x
y
-plane. Which of the following statements correctly describes the graph of the line?
\newline
Choose
1
1
1
answer:
\newline
(A) The line has a negative
y
y
y
intercept.
\newline
(B) The line goes through the point
(
0
,
3.4
)
(0,3.4)
(
0
,
3.4
)
.
\newline
(C) The line has a positive slope.
\newline
(D) The line is perpendicular to the
y
y
y
-axis.
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The equation
y
=
3
2
(
x
−
8
)
y=\frac{3}{2}(x-8)
y
=
2
3
(
x
−
8
)
is graphed in the
x
y
x y
x
y
-plane. Which of the following equations will have a graph that is parallel to the graph of the given equation and have an
x
x
x
intercept on the negative
x
x
x
-axis?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
3
2
(
x
+
8
)
y=\frac{3}{2}(x+8)
y
=
2
3
(
x
+
8
)
\newline
(B)
y
=
3
2
x
−
8
y=\frac{3}{2} x-8
y
=
2
3
x
−
8
\newline
(C)
y
=
−
2
3
(
x
+
8
)
y=-\frac{2}{3}(x+8)
y
=
−
3
2
(
x
+
8
)
\newline
(D)
y
=
−
2
3
x
−
8
y=-\frac{2}{3} x-8
y
=
−
3
2
x
−
8
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The equations
2
y
=
−
4
x
+
8
2 y=-4 x+8
2
y
=
−
4
x
+
8
and
2
y
=
−
4
x
+
16
2 y=-4 x+16
2
y
=
−
4
x
+
16
are graphed in the
x
y
x y
x
y
-plane. Which of the following must be true of the graphs of the two equations?
\newline
Choose
1
1
1
answer:
\newline
(A) The graphs of the two equations are parallel lines.
\newline
(B) The graphs of the two equations are perpendicular lines.
\newline
(C) The graphs have the same
y
y
y
-intercept.
\newline
(D) The
y
y
y
-intercepts of the two graphs are reflected in the
x
x
x
-axis.
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Which of the following is an equation of the line in the
x
y
x y
x
y
plane with
x
x
x
-intercept
−
2
7
-\frac{2}{7}
−
7
2
and
y
y
y
intercept
8
7
\frac{8}{7}
7
8
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
y
−
28
x
=
8
7 y-28 x=8
7
y
−
28
x
=
8
\newline
(B)
7
y
+
28
x
=
8
7 y+28 x=8
7
y
+
28
x
=
8
\newline
(C)
−
7
y
+
28
x
=
8
-7 y+28 x=8
−
7
y
+
28
x
=
8
\newline
(D)
−
7
y
−
28
x
=
8
-7 y-28 x=8
−
7
y
−
28
x
=
8
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Which of the following is an equation of the line in the
x
y
x y
x
y
plane with
x
x
x
-intercept
5
3
\frac{5}{3}
3
5
and
y
y
y
intercept
10
7
\frac{10}{7}
7
10
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
7
y
+
6
x
=
10
-7 y+6 x=10
−
7
y
+
6
x
=
10
\newline
(B)
7
y
+
6
x
=
−
10
7 y+6 x=-10
7
y
+
6
x
=
−
10
\newline
(C)
7
y
+
6
x
=
10
7 y+6 x=10
7
y
+
6
x
=
10
\newline
(D)
7
y
−
6
x
=
10
7 y-6 x=10
7
y
−
6
x
=
10
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(
x
+
3
)
2
+
(
y
−
4
)
2
=
9
(x+3)^{2}+(y-4)^{2}=9
(
x
+
3
)
2
+
(
y
−
4
)
2
=
9
\newline
A circle in the
x
y
x y
x
y
-plane has the equation shown. If the
x
x
x
coordinate of a point on the circle is
−
3
-3
−
3
, what is a possible corresponding
y
y
y
-coordinate?
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