Name __________________________________
Date ________________________ Hour ______
Algebra 2: Quadratics Review (last one)
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1.
I can interpret key features of graphs and tables.
I can sketch graphs showing and identifying the key features.
I can graph a quadratic functions and show intercepts (zeroes), max/min, and end
behavior.
Graph the function and use it to determine the following key features:
y = x2 + 2x – 8
y-a x is
10
9
Use a RED marker to label the xintercept(s) and write the coordinate(s):
8
7
6
Use a BLUE marker to label the yintercept(s) and write the coordinate(s):
Use a GREEN marker to draw the line of
symmetry and write the equation:
5
4
3
2
1
-10 -9
-8
-7
-6
-5
-4
-3
-2
-1
1
-1
Use an ORANGE marker to label the
maximum/minimum and write the
coordinate:
-2
-3
-4
-5
-6
-7
-8
-9
Describe the end
behavior:
As x -, f(x) _______
As x +, f(x) _______
Increasing interval
Decreasing interval
Domain
Range
-10
2
3
4
5
6
7
8
9
10
x -a xis
I can determine if an ordered pair is a solution to an equation or a graph.
2.
The function y = f(x) is graphed here.
a) Plot three points that are solutions to y = f(x). Explain how you know these are solutions to y = f(x).
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b) Plot all points that are solutions to f(x) = 0. Explain how you know these are solutions to f(x) = 0.
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I can identify the effect of transformations of a graph when given the equation.
3. If f(x) = x2, then the graph of each equation below is a parabola. Describe the transformation of
the parabola relative to the graph of the parent function. Be sure to give the direction of the
transformation and explain how the x- or y-values change.
𝑦 = 𝑓(𝑥) + 1
𝑦 = 𝑓(𝑥 + 2)
1
𝑦 = 𝑓( 𝑥)
3
I can write the equation of a function when given a transformed graph.
4.
a.)
Given the transformed graph, write the equation for the graph.
b.)
Equation: ________________________
Equation: _________________________
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I can use factoring in a quadratic function to show zeros of the graph, and interpret
these in terms of a context.
I can use completing the square to show max/min (vertex) and symmetry of a graph,
and interpret these in terms of a context.
5.
Use the following situation for questions below. The formula for the height of a thrown object
can be approximated by the formula: h(t )  16t 2  v0t  h0 where h(t) is the height of the ball in feet
after t seconds, v0 is the initial velocity in feet/second and h0 is the initial height in feet. Suppose a
pebble is thrown from a 20 foot cliff with an initial velocity of 22 ft/s.
a)
Write a quadratic function to model the height of the pebble after t seconds.
b)
What are the zeros of the function? What does that tell us about the pebble?
c)
What is the vertex (maximum) of the function? What does that tell us about the pebble?
I can perform operations with complex numbers.
6.
Simplify the following complex expressions. Leave your answer in a + bi form.
a)
(12 – 5i) – (8 – 3i)
b)
(5 – 4i)(7 – 2i)
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7.
I can solve quadratic equations by taking square roots, completing the
square, quadratic formula, and factoring.
I can recognize when a quadratic equation gives complex solutions.
I can solve quadratic equations with complex solutions.
I can write complex solutions to quadratic equations in the form a ± bi.
Solve using any method.
a. 𝑥 2 + 6𝑥 + 2 = 0
I chose to solve by _____________________
(factoring, completing the square, quadratic formula,
taking square roots, graphing)
because___________________________________
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b. 3𝑥 2 + 6𝑥 = −5
I chose to solve by _____________________
(factoring, completing the square, quadratic formula,
taking square roots, graphing)
because___________________________________
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c. (𝑥 + 1)2 = −16
I chose to solve by _____________________
(factoring, completing the square, quadratic formula,
taking square roots, graphing)
because___________________________________
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I can solve quadratic equations by taking square roots, completing the square,
quadratic formula, and factoring.
8.
Given the following functions, which of them has -3 as zero? Explain your reasoning.
Explanation
𝑓(𝑥) = 𝑥 2 − 2𝑥 − 15
𝑓(𝑥) = 𝑥 2 − 9
𝑓(𝑥) = 2𝑥 2 − 3𝑥 − 9
𝑓(𝑥) = (𝑥 − 3)2 − 1
I can compare properties of two or more functions.
9.
Use the three different functions given in different forms below:
A)
B)
f(x) =
x2
+ 2x – 5
C)
x
-5
-4
-3
-2
-1
0
1
y
7
0
-5
-8
-9
-8
-5
a) Which function, A or B, has the least (smallest) minimum value? Explain your answer.
b) Which function, A or C, has the smallest zero? Explain your answer.
c) Which function, A, B, or C, has the smallest (lowest) y-intercept? Explain your answer.
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I can solve quadratic equations by taking square roots, completing the
square, quadratic formula, and factoring.
I can recognize when a quadratic equation gives complex solutions.
I can solve quadratic equations with complex solutions.
I can write complex solutions to quadratic equations in the form a ± bi.
10.
Write and solve a quadratic equation that has:
a)
two real solutions
b)
1 real solution
c)
two non-real solutions
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11.
I can write a quadratic model from given data values.
I can use the model to make predictions.
I can analyze residuals to assess the fit of the regression curve.
Use the following data to answer the questions below.
Automobile Stopping Distance: Selected values of the stopping distance y in feet of a car traveling
x miles per hour are given in the table.
Speed (mph), x
20
30
40
50
60
70
Stopping Distance
(feet), y
46
87
140
240
282
371
a)
Put the data on your graphing calculator and write a quadratic regression equation for the data.
b)
Is a quadratic model a good fit for this model? Explain using the residual plot.
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c)
If you found that f(100) = 345, what would that mean in the context of the problem? Do you
think that is a reasonable prediction? Why or why not?
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