ENHANCED MATH II
Module 2  Practice Problems
1. Which one of the following translates the function
a)
f ( x ) = 3x 2 − 5
d)
f ( x ) = x2 + 3 − 5
(
b)
)
f ( x ) = x 2 − 5 three units to the left?
f ( x ) = ( x + 3 )2 − 5
c)
f ( x ) = ( x − 3 )2 − 5
e) none of these
Problems 2, 3, 4. Refer to the figure shown.
2. Describe the transformations undergone by the parabola y =
3 2
x
16
to obtain the parabola shown.
a) 1. reflection about the x-axis
2. translate 2 units left
3. translate 3 units up
b) 1. reflection about the y-axis
2. translate 3 units right
3. translate 2 units down
c) 1. reflection about the x-axis
2. translate 3 units left
3. translate 2 units up
d) 1. reflection about the y-axis
2. translate 2 units right
3. translate 3 units down
e) what?, we never learned this!
3. What is the axis of symmetry of the parabola shown?
4. What is the vertex of the parabola shown?
2
Problems 5, 6, 7, 8, 9, 10. These problems use the function: f(x) = −7x + 56x − 111
5. What is the maximum or minimum value of f(x) ?
6. What is the vertex of f(x) ?
7. What is the y-intercept of f(x) ?
8. What is the Vertex-Form of f(x) ?
9. What are the x-intercepts of f(x) ?
10. What is the Range of f(x) ?
11. The function f ( x ) = ( x − 4 ) 2 is reflected across the y-axis, vertically stretched by a factor of 3, and translated 5
units up to create the function g. Write function g? (Follow the order of the transformations to obtain the answer)
12. What is the vertex of function g in problem 11?
13. A rectangle has a perimeter of 100 cm. Find the greatest possible area for the rectangle.
2
a) 625 cm
2
b) 600 cm
14. Factor completely:
9z2 − 66z + 121
15. Factor completely:
75 x3 y − 27 x y 3
2
c) 400 cm
2
d) 225 cm
2
e) 49 cm
( x − 4 )2 − y2
16. Factor completely:
17. Solve for x: 0 = 4 ( x − 6 )2 − 7
7
3
18. Solve for x: 0 = 8 ( x + 1)2 + 3
3
5
Problems 19 and 20. These problems use the function: f ( x ) = − 9 ( x − 2 ) 2 + 1
f ( x ) = ax 2 + bx + c
19. What is the value of b in the Standard Form f(x) ?
a) 36
b) −36
c) 18
Standard Form:
d) −18
e) −35
d) −18
e) −35
20. What is the value of c in the Standard Form f(x) ?
a) 36
b) −36
c) 18
21. Points (−1, −5), (3, −1), and (4, −15) are found on the graph of a quadratic function of the form y = ax 2 + bx + c .
Which one of the following is the correct sum of the coefficients (i.e. a + b + c) of the function containing these
Points?
a) 9
b) −9
c) −6
d) 6
e) 4
22. Which one of the following represents the area of the
figure shown?
a) 9 x 2 + 14 x + 2
b) 9 x 2 + 8 x + 4
c) 9 x 2 + 6 x + 2
d) 9 x 2 + 14 x + 4
e) 9 x 2 + 8 x + 2
23. Determine the “works” for
y=−
4 2
4
56
x +
x+
5
15
15
Problems 24, 25, 26 and 27 . Use  f ( x ) = 9 x − 5
2
24.
Function h( x ) is obtained by translating f ( x ) 4 units to the left. Write the function h( x ) in Vertex Form.
25.
Function h( x ) is obtained by translating f ( x ) 8 units down. Write the function h( x ) in Vertex Form.
26.
Function h( x ) is obtained by reflecting f ( x ) about the x-axis. Write the function h( x ) in Vertex Form.
27.
Function h( x ) is obtained by reflecting f ( x ) about the y-axis. Write the function h( x ) in Vertex Form.
4
( x − 6 ) 2 + 2 is reflected across the y-axis and moved up 3 units to obtain the
3
new function n( x ) . Write the new function n( x ) in Vertex-Form. Follow the order of the transformations.
28. The function g ( x ) = −
29. The function g ( x ) = 8 ( x + 1 ) − 7 is reflected across the x-axis and stretched by a factor of 3 to obtain the
2
new function n( x ) . Write the new function n( x ) in Vertex-Form. Follow the order of the transformations.
Do the functions g ( x ) and n( x ) have the same x and y intercepts?
A quadratic equation that has x-intercepts of (−2 , 0) and (8 , 0), a vertical stretch of 3, and the
vertex is a minimum. Determine the following:
a. Factored form equation
b. Vertex form equation
Other:
1. Examine the following sequence: 1, 11, 111, 1111, . . .
In other words, f ( 1 ) = 1 , f ( 2 ) = 11 , f ( 3 ) = 111 , and so on.
Write a recursive formula to obtain the nth term  f ( n ) = ?
c. Standard form equation