Name ____________________________________________ Date __________________
Review of Graphing Quadratics and Best Fit Lines/Curves
Directions: Graph each quadratic. Answer the questions provided.
𝒚 = 𝟐𝒙𝟐 + 𝟒𝒙 − 𝟔
1.
Does the parabola open up or down?
Vertex
a=
b=
Is the vertex a minimum point or a maximum point?
Table of Values
c=
x
Equation of Axis of
Symmetry
y
Roots
2. Look at the graph below. Determine the roots, the vertex, and the
equation of the axis of symmetry.
Based on the graph, is the “a” value for the equation positive or negative? How do you
know?
Vertex
Roots
Equation of Axis of Symmetry
3. Using the equation of the line of best fit, which number is the best
prediction of the output when the input is 13?
Linear Regression
Calculator
{(-5, 9), (0, 42), (2, 31), (5, 97), (9, 143), (11, 151)}
Quadratic Regression
Calculator
a. 127
b. 159
c. 170
d. 178
4. What is the curve of best fit for the scatter plot shown below?
a.
y = 62.15x2 + 140.32x – 9.35
b.
y = -56.21x2 + 139.31x + 9.35
c.
y = -1.22x + 56
d.
y = 56x – 1.22
5. What is the line of best fit for the scatter plot shown to the right?
a. y = -32.07x2 + 68.9x + 8.3
b. y = -3.02x + 0.01
c. y = 50.45x2 – 117.14x + 2.54
d. y = 2.1x + 0.14
6. A scientist dropped an object from a height of 200 feet. She recorded the height in 0.5second intervals. Her data is shown.
Time
(seconds)
Height
(feet)
0.0
0.5
1.0
1.5
2.0
2.5
200
195
185
165
135
100
Based on a quadratic model, what is the approximate height of the object at 3 seconds?
7. Kim and Sandy are lifeguards at the pool. They wanted to find the relation between the
temperature (𝐹°) and the number of people that came swimming. The data is shown in the
chart below.
Temperature 78
# of People
40
Swimming
79
46
82
50
82
54
85
62
90
70
93
72
94
79
96
88
97
88
98
91
a. Describe the relationship between the temperature and the number of people swimming.
How do you know it is a linear relationship?
b. Use the calculator to determine the equation of the best fit line. Round to the nearest 100th.
c. Using the equation, determine how many people would be swimming when the temperature
is 88°.
d. Using the equation, determine the temperature if 58 people are swimming.
8. The table below represents the height of a ball after it has traveled a certain distance.
a. Determine the curve of best fit (quadratic regression) for the data listed in the table. Round to
the nearest hundredth if necessary.
b. Determine the height of the ball if it travels 30 meters.
c. Determine the height of the ball if it travels 50 meters.
Distance
(m)
Height
(m)
7
8
20
15
33
24
47
26
60
24
67
21