AFDA
Quarter 2 Cumulative Assessment
Review Packet
Block __
Name:____________________
Calculator Page
Quadratic Formula: 𝑥 =
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
Regression and Calculator
STEP 1—General Set-up
2nd 0 (CATALOG)
x1−
Scroll to find DiagnosticOn
ENTER
ENTER
Y=
Y1= is empty
Plot 1 is highlighted
STEP 2—Entering Data/Viewing Graph
STAT
1: Edit
(enter data into L1 and L2)
ZOOM
9: ZoomStat
**determine based on graph shape which regression to run
STEP 3—Equation
STAT
CALC (based on the shape of your graph, choose which regression curve to select)
4: LinReg (ax+b)
5:QuadReg
9:LnReg
0:ExpReg
StoreRegEq:
VARS
Y-VARS
1:Function
1:Y1
ENTER
**The line of best fit should now be stored in your Y=, Y1, allowing you to use your table to
find data points
Part I: Unit 3 – Absolute Value and Piecewise Functions
1. Solve. −2|3𝑥 − 1| = −8
2. Solve. |3𝑥 + 5| + 6 = −2
3. For the following inequality, solve, graph on the given number line, and write the
solution in interval notation:
|2𝑥 − 1| + 7 > 18
Interval Notation:______________
4. For the following inequality, solve, graph on the given number line, and write the
solution in interval notation:
−4|𝑥 + 3| − 1 ≥ −13
Interval Notation:______________
5. At the ACME Graphics Company, the average starting salary for a new graphic
designer is $38,000, but the actual salary could differ from the average by as much
as $3,590. What is the range of salaries for a new graphic designer? Define the
variable, write an absolute value inequality statement modeling the situation, and
solve.
6. The ideal diameter of a piston for one particular type of car is 76 mm, but the
measurement can vary from the ideal at most by .075 mm. What is the acceptable
range of diameters for the piston? Define the variable, write an absolute value
inequality statement modeling the situation, and solve. Write an absolute value
inequality and then find the range of acceptable diameters for the piston.
7. Graph the function. Identify the vertex, axis of symmetry, and translations in the
space provided.
𝑦 = 3|𝑥 − 4| − 6
Vertex: ________
AoS: _________
Translations from parent graph:
8. Graph the function. Identify the vertex, axis of symmetry, and translations in the
space provided.
𝑦 = −|𝑥 + 5| + 4
Vertex: ________
AoS: _________
Translations from parent graph:
9. Identify the vertex, axis of symmetry, and graph the function.
3
𝑓(𝑥) < |𝑥 + 1| − 5
4
Vertex: ________
AoS: _________
Test for shading:
10.
Identify the vertex, axis of symmetry, and graph the function.
𝑓(𝑥) ≥ −|𝑥 − 3| + 4
Vertex: ________
Test for shading:
AoS: _________
11.
Graph the following piece-wise function.
2𝑥 − 4,
𝑓(𝑥) = {
−5𝑥 + 1,
12.
𝑥>2
𝑥≤2
Graph the following piece-wise function.
−2𝑥 − 3,
4,
𝑓(𝑥) = {
3𝑥 − 1,
𝑥 ≤ −1
−1 < 𝑥 ≤ 1
𝑥>1
13. Mr. Sipe has to order food for the basketball teams. McTaco Hut charges an initial
service fee of $30 for a group order, and for an order of 25 or fewer meals it’s
$7.50 per meal, and for orders of more than 25 meals, it is $5.75 per meal.
a. Write a piecewise function that gives the cost, C, for an order of x amount of
meals.
b. If 18 people wanted to purchase a meal, how much would Mr. Sipe pay in
total?
14. A group of friends is renting a limo for prom. Panther Limo Company charges a flat
fee of $50 for convenience charge, a limo ride for three or fewer hours is $68 an
hour and a ride over three hours is $52 an hour.
a. Write a piecewise function that gives the cost, C, for an order of x number of
hours renting the limo.
b. If the group spends 6 hours in the limo, how much will the ride cost?
Part II: Quadratic Functions
Directions: Given the quadratic in vertex form, fill out all the information and graph.
15. 𝑓(𝑥) = (𝑥 − 1)2 − 5
𝑥
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
(Min or Max)
𝑓(𝑥)
Translations:
D:___________R: ____________
Zero(s): ______________ Y int.: __________
16. 𝑓(𝑥) = −2(𝑥 + 3)2 + 4
𝑥
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
(Min or Max)
𝑓(𝑥)
Translations:
D:___________R: ____________
X-Int.(s): ______________ Y int.: __________
Directions: Given the quadratic in intercept form, fill out all the information and graph.
17. 𝑓(𝑥) = −(𝑥 + 1)(𝑥 − 5)
𝑥
𝑓(𝑥)
Direction:
AOS:
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
Root(s): ______________ Y int.: __________
18. 𝑓(𝑥) = (𝑥 + 7)(𝑥 + 2)
𝑥
𝑓(𝑥)
Direction:
AOS:
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
Solution(s): ____________ Y int.: _________
Directions: Given the quadratic in standard form, fill out all the information and graph.
19.
1
𝑓(𝑥) = − 𝑥 2 + 2x + 1
4
𝑥
𝑓(𝑥)
Direction:
AOS:
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
Root(s): ______________ Y int.: __________
20. 𝑓(𝑥) = 3𝑥 2 − 3𝑥 + 2
𝑥
𝑓(𝑥)
Direction:
AOS:
Vertex:
(Min or Max)
Translations:
D:___________R: ____________
X-int.(s): ______________ Y int.: __________
21.
An athlete throws a shot put with an initial vertical velocity of 40 feet
per second, as modeled by the equation ℎ = −16𝑡 2 + 40𝑥 + 6.5,
where h is the height in feet and t is the time in seconds. At what time
does the shot put reach the maximum height? What is the maximum
height?
22.
Students are selling packages of flower bulbs to raise money for a
class trip. The sales revenue R (in dollars) generated by selling the
packages is given by the function 𝑦 = −10𝑛2 + 100𝑛 + 750 where n is
the price per package. What should the students charge per package
to maximize profit?
23.
Find the discriminant of the following problems. State the nature of the
solutions and the number of solutions. Then, solve using the quadratic
formula. Lastly, draw a quick sketch of the graph.
**REMEMBER! Must be in standard form first!
4𝑥 2 − 5 = 8𝑥
𝑎=
Discriminant and # of Solutions
2𝑥 2 + 𝑥 = 3
Discriminant and # of Solutions
𝑏=
𝑐=
Quadratic Formula
𝑎=
𝑏=
Rough Sketch of Graph
𝑐=
Quadratic Formula
Rough Sketch of Graph
24.
The table shows how wind affects a runner’s performance in the 200 meter dash.
Positive wind speeds correspond to tailwinds, and negative wind speeds
correspond to headwinds. The change t in finishing time is the difference
between the runner’s time when the wind speed is s and the runner’s time when
there is no wind.
Wind speed (m/sec), s
Change in finishing time (sec), t
-6
2.28
-4
1.42
-2
0.67
0
0
2
-0.57
4
-1.05
6
-1.42
a) What is the quadratic equation of the regression model of best fit? Round to
three decimals
b) What is the 𝑟 2 value? What does this mean? Round to three decimals.
c) Predict the change in finishing time if the wind is 10 m/second? Is the
interpolation or extrapolation?