Download Solutions - SD308.org

Mid-Chapter Quiz
Use a table of values to graph each equation. State the domain and range.
2
1. y = x + 3x + 1
SOLUTION: x
y
1
−3
−2
−1
−1
−1
0
1
1
5
2
11
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y|y ≥
−1.25}.
2
2. y = 2x − 4x + 3
SOLUTION: 2
x
2x − 4x + 3
2
−3
2(−3) − 4(−3) + 3
33
2
19
2
9
2
3
2
1
2
3
−2
2(−2) − 4(−2) + 3
−1
2(−1) − 4(−1) + 3
0
2(0) − 4(0) + 3
1
2(1) − 4(1) + 3
2
y
2(2) − 4(2) + 3
2
9
2(3) − 4(3) + 3
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
3
The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y|y ≥ 1}.
eSolutions Manual - Powered by Cognero
Page 1
2
3. y = −x − 3x − 3
The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y|y ≥
Mid-Chapter
Quiz
−1.25}.
2
2. y = 2x − 4x + 3
SOLUTION: 2
x
2x − 4x + 3
2
−3
2(−3) − 4(−3) + 3
y
33
2
19
2
9
2
3
2
1
2
3
−2
2(−2) − 4(−2) + 3
−1
2(−1) − 4(−1) + 3
0
2(0) − 4(0) + 3
1
2(1) − 4(1) + 3
2
2(2) − 4(2) + 3
2
9
2(3) − 4(3) + 3
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
3
The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y|y ≥ 1}.
2
3. y = −x − 3x − 3
SOLUTION: 2
x
−x − 3x − 3
2
−3
− (−3) − 3(−3) − 3
−2
y
−3
2
−1
2
−1
2
−3
2
−7
− (−2) − 3(−2) − 3
−1
− (−1) − 3(−1) − 3
0
− (0) − 3(0) − 3
1
− (1) − 3(1) − 3
2
−13
− (2) − 3(2) − 3
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
2
The domain is all real numbers. The range is all real numbers less than or equal to the maximum value, or {y|y ≤
eSolutions
Manual - Powered by Cognero
−0.75}.
2
4. y = −3x − x + 1
Page 2
The domainQuiz
is all real numbers. The range is all real numbers greater than or equal to the minimum value, or {y|y ≥ Mid-Chapter
1}.
2
3. y = −x − 3x − 3
SOLUTION: 2
x
−x − 3x − 3
2
−3
− (−3) − 3(−3) − 3
y
−3
2
−1
2
−1
2
−3
2
−7
−2
− (−2) − 3(−2) − 3
−1
− (−1) − 3(−1) − 3
0
− (0) − 3(0) − 3
1
− (1) − 3(1) − 3
2
−13
− (2) − 3(2) − 3
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
2
The domain is all real numbers. The range is all real numbers less than or equal to the maximum value, or {y|y ≤
−0.75}.
2
4. y = −3x − x + 1
SOLUTION: 2
x
−3x − x + 1
2
−3
−3(−3) − (−3) + 1
y
−23
2
−9
2
−1
2
1
2
−3
−2
−3(−2) − (−2) + 1
−1
−3(−1) − (−1) + 1
0
−3(0) − (0) + 1
1
−3(1) − (1) + 1
2
−13
−3(2) − (2) + 1
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
2
The domain is all real numbers. The range is all real numbers less than or equal to the maximum value,
eSolutions Manual - Powered by Cognero
or
.
2
Page 3
The domainQuiz
is all real numbers. The range is all real numbers less than or equal to the maximum value, or {y|y ≤
Mid-Chapter
−0.75}.
2
4. y = −3x − x + 1
SOLUTION: 2
x
−3x − x + 1
2
−3
−3(−3) − (−3) + 1
y
−23
2
−9
2
−1
2
1
2
−3
−2
−3(−2) − (−2) + 1
−1
−3(−1) − (−1) + 1
0
−3(0) − (0) + 1
1
−3(1) − (1) + 1
2
−13
−3(2) − (2) + 1
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
2
The domain is all real numbers. The range is all real numbers less than or equal to the maximum value,
or
.
2
Consider y = x − 5x + 4.
5. Write the equation of the axis of symmetry.
SOLUTION: To find the axis of symmetry, use the equation
. For this equation, a = 1 and b = − 5. So,
6. Find the coordinates of the vertex. Is the vertex a maximum or minimum point?
SOLUTION: The vertex goes through the line of symmetry.
To find the axis of symmetry, use the equation
. For this equation, a = 1 and b = − 5. So,
eSolutions
Manual - Powered by Cognero
So the x-value is 2.5. Substitute this into the equation to determine the y-value.
Page 4
Mid-Chapter Quiz
6. Find the coordinates of the vertex. Is the vertex a maximum or minimum point?
SOLUTION: The vertex goes through the line of symmetry.
To find the axis of symmetry, use the equation
. For this equation, a = 1 and b = − 5. So,
So the x-value is 2.5. Substitute this into the equation to determine the y-value.
So, the vertex is (2.5, −2.25). Because a > 0, the graph opens upward and the vertex is a minimum.
7. Graph the function.
SOLUTION: x
y = x 2 - 5x +
4
2
−1
(−1) − 5(−1)
y
10
+4
0
2
4
2
0
2
−2
2
−2
(0) − 5(0) + 4
1
(1) − 5(1) + 4
2
(2) − 5(2) + 4
3
(3) − 5(3) + 4
2
0
(4) − 5(4) + 4
Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.
4
eSolutions Manual - Powered by Cognero
Page 5