Name:______________________________________
Algebra 2 Chapter 4 Test Review
1. How many real roots does the graph have (can be rational or irrational)?
a.
f  x   6 x 2  5x  4
b.
f  x   2x2  6x  1
c.
f x   2 x 2  5 x  4
d.
f  x   x 2  10 x  25
2. Draw a quick sketch of a quadratic function with:
a. A positive discriminant
b. A negative discriminant
c. A discriminant that is zero
For #3-4, answer the following:
a. What are the roots of each function?
b. The discriminant of each function would be classified as positive, negative, or zero?
c. Identify the vertex and the axis of symmetry.
d. Identify the transformations from the parent function y  x 2
e. Write the equation of each function in vertex form:
3.
a. __________________________________________
b. __________________________________________
c. __________________________________________
d.
e. __________________________________________
4.
a. __________________________________________
b. __________________________________________
c. __________________________________________
d.
e. __________________________________________
2
5. Arnold says that the function graphed to the right could be the graph of f  x   x  x  5 .
Use the discriminant of the function to agree or disagree with Arnold.
6. a. Would the discriminant of the function below be positive, negative, or zero?
b. Write a possible equation for the function in standard form using the zeros:
c. On the graph to the right, sketch y  2 x  6 and identify the points of intersection
with the parabola:
7. Multiple Choice: If the graph of f ( x )  x 2 is shifted 3 units to the left and reflected over the x-axis, circle
the correct equation of the new graph:
a.
g ( x)   ( x  3)2
b. g ( x)   ( x  3) 2
c. g ( x)   x 2  3
d. g ( x)   x 2  3
8. Multiple Choice: If the graph of f ( x )  x 2 is shifted 4 units up and vertically compressed/shrunk by ½,
circle the correct equation of the new graph:
b.
g ( x)   2 x 2  4
b. g ( x )  
1 2
x 4
2
1
2
2
c. g ( x)  ( x  4)
d. g ( x ) 
9. Write an equation of a quadratic function in vertex form that has the following characteristics:
 Vertex at (3, 1)


Stretched vertically by 4
Reflected over the x-axis
10. For the given equation, check all of the following that apply: f ( x)  4( x  8) 2  12






Parabola opens up
Parabola open down
Vertex is a maximum
Vertex is a minimum
Vertical stretch
Vertical shrink
1 2
x 4
2
3
( x  7) 2  10
4
11. For the given equation, check all of the following transformations: f ( x)  






Reflection over the x-axis
Reflection over the y-axis
Rotation around Quadrant I
Vertical stretch by ¾
Vertical shrink by ¾
Horizontal shrink by 7






Shift 7 units left
Shift 7 units right
Shift 7 units up
Shift 10 unit right
Shift 10 units up
Shift 10 units down
12. Find the vertex of the given functions:
a.
c.
1
f ( x)  x 2  6 x
2
3
f ( x)   x 2  7
5
b. f ( x)  3x 2  4 x  5
2
d. f ( x)   ( x  5) 
3
4
13. Sketch f ( x)  x 2  4 x  1
Identify the vertex: _____________________________
Identify the axis of symmetry: _________________
Find y-intercept: ________________
Domain:____________________
Range:______________________
Transformations:
Rewrite f(x) in vertex form by completing the square (show all steps):
Did you get the same vertex?
14. Given f ( x)  3x 2  12 x  8
a. Show all the steps needed to rewrite f(x) in vertex form by completing the square:
b. Identify the vertex of f(x) from your vertex form:_________________________
c. Verify by finding the vertex from standard form:
d. Graph f(x)
e. Identify the domain and range:
f.
Sketch g ( x )  x  6 on the same graph and identify the
points of intersection with f(x):
15. Given f ( x)   x 2  8 x  15
a. Show all the steps needed to rewrite f(x) in vertex form by completing the square:
b. Identify the vertex of f(x): _________________________
c. Graph f(x):
d. Solve the equation by factoring: x 2  15  8 x
e. Where can you find your solutions on the graph?
16. How can you tell if a quadratic equation is factorable?
For #17-22, solve each quadratic equation. Make sure you use each of the following methods at least once:
 Factor
 Complete the Square
 Quadratic Formula
17. 3 x 2  6 x  3  0
18. 5 x 2  8 x  8
19. x 2  4 x  2  0
20. x 2  12 x  36
21. 3 x 2  4 x  6  0
22. 7 x 2  28  0