Algebra 2
Quadratic Functions and Graphs Review
Name
UQ: What is the relationship between an equation and a graph of a quadratic function?
Covered Concepts:
Relating roots (zeros) to the graph of a quadratic function
Identify properties of quadratics (max/min, intervals of increasing/decreasing, roots, lines of symmetry, vertex)
Graphing and translating quadratics in vertex form
Identify domain and range of functions
Using regression models to make predictions about trends in data
Finding Inverses of relations and functions
1.
If the only solution to a quadratic function is x = 4, what can we conclude about its graph?
If the two solutions to a quadratic function are x = -2 and x = 3, what can we conclude about its graph?
If the two solutions to a quadratic function are x = 2i and -2i, what can we conclude about its graph?
2. Given the following equations, identify the vertex and whether it is a maximum or a minimum.
Y = 2(x – 3)2 – 6
y = -5x2 + 6
y = x2 – 7
3. Given the function y = x2 + x + 1, use the discriminant to determine how many solutions, what type of solutions
exist and how many times does the graph cross the x-axis.
Discriminant:
How many solutions:
Circle one:
solution(s) are real
solutions are imaginary
How many times does it cross the x-axis __________________________
4. Given the following xy table, identify the domain and range.
X
0
-2
0
Y
1
2
1
Domain =
Range =
-2
4
0
5
5.
Identify the vertex, the line of symmetry, the roots (zeroes) of the function and the intervals of increase and
decrease.
y
Vertex:
4
3
Line of Symmetry (Equation):
2
Roots
1
x
-4
-3
-2
-1
1
2
3
4
Interval of Increase:
-1
Interval of Decrease:
-2
-3
Domain : ______________________
-4
Range: ________________________
6. Use the graph of y = x2 to answer the following questions.
a. If you translate the parabola 2 units left and 7 units up , what is the equation of the new parabola in vertex
form?
b. If you translate the original parabola to the 2 units right and 6 units down, what is the equation for the new
parabola in vertex form?
7. Use the graph of y = -(x – 3)2 + 1 to answer the following questions.
a. If you translate the parabola 3 units left and 5 units up, what is the equation of the new parabola in vertex
form?
b. If you translate the original parabola 4 units right and 2 units down, what is the equation of the new
parabola in vertex form?
8. Given the following equation: y = 2(x – 3)2+ 4 Complete the information below to explain how the original graph of
y = x2 has been translated.
Circle one:
left or right
how many ___________
Circle one:
narrower, wider, or unchanged
Circle one:
the parabola
has
or
has not
been inverted.
9.
a. Graph the function:
𝑦 = −2(𝑥 + 3)2 + 2.
b. Identify the maximum value
10.
c.
Identify the domain:
d.
Identify the range:
Use the graph at right to answer the questions.
y
6
a. Write the equation of the parabola in vertex form.
5
4
Equation:
3
y=
2
1
x
-6
b. Identify the domain and range for this function.
-5
-4
-3
-2
-1
1
2
3
4
5
6
-1
-2
Domain =
-3
-4
Range =
-5
-6
11. Given the function y = -3(x – 4)2 + 2, identify the vertex.
12. Given the function y = (x + 4)2 – 2, identify the vertex.
13. Would the function y = 4x2 + 7x – 12 have a maximum or a minimum value? Explain how you could determine this
without graphing the function.
14. Given the function y = 4x + 6, identify the inverse function y-1.
15. Given the function y = 2x2 – 5, identify the inverse function y-1.
16. The graph of a function f(x) is shown below. On the same graph,
draw a graph that represents f-1(x)?
17. The graph of a function f(x) is shown below. On the same graph
y
5
draw a graph that represents f-1(x)?
4
3
2
1
x
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
2
3
4
5
18. Open ended. Suppose you hit a baseball and its flight takes a parabolic path. The height of the ball at certain
times appears in the table.
Time (seconds)
0.5
0.75
1
1.25
a.
Height (ft)
10
10.5
9
5.5
Place the data in the calculator and find an appropriate regression model.
Regression Model
b. Using your equation, predict the height of the ball at .85 seconds.
b. Using your equation, predict what the height of the ball will be after 3 seconds. Explain your
answer.