1) give exact and approximate solutions to three decimal places
x2  7x  5  0
Exact solution x =
7  29 7  29
,
2
2
Approximate solutions to three decimal places x = 0.807,6.193
2) A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the
rectangle. What is the maximum area that the farmer can enclose with 80ft fence? What should the
dimensions of the garden give this area?
Maximum area that the farmer can enclose with 80ft of fence is 800 square feet
The dimensions of the garden to give this area is 40ft by 20 ft
3) Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and
graph the function f(x)= - x ^2 + 12x + 3
The vertex is (6, 39)
The equation of the line of symmetry is x = 6
The maximum/minimum of f(x) is 39
The value of f(6)=39 is which of the following?
Maximum?
40
y
30
20
10
x
0
-40
-30
-20
-10
0
10
20
30
40
-10
-20
-30
-40
4) Determine the nature of the solutions of the equation
y2 
3
2
y
7
7
The equation has two real solutions?
5)a) solve 3 x 2  7 x  5  0
What are the solutions? (type exact answers. Express complex numbers in terms of i. use comma to
separate answers)
7  109 7  109
,
6
6
5b) find the x-intercepts of f ( x)  3x 2  7 x  5
What are the x-intercepts (type an ordered pair. Simplify your answer. Type an exact answer. Express
complex numbers in terms of i. use comma to separate answers)
 7  109   7  109 

,0 , 
,0 

6
6



6) write a quadratic equation in the variable x having the given numbers as solutions. Type the equation
in standard form, ax 2  bx  c  0
Solution 9, only solution
The equation is x2 - 18x + 81 = 0
7) Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the
function. f ( x)  ( x  8) 2  5
The vertex is (8, 5)
The line of symmetry is x = 8
The value of f(-8)=-5, is? False
Maximum
8) Give exact and approximate solutions to three decimal places
x 2  4 x  4  25
What are the exact solutions? -7, 3
Type an exact answer, using the radicals as needed. Rationalize all denominators. Express complex
numbers in terms of i. use a comma to separate answers as needed.
9) determine the nature of the solutions of the equation. x 2  18 x  81  0 . What does the equation
have?
b)one real solution?
10) Give exact and approximate solutions to three decimal places. ( x  9) 2  12
What are the exact solutions? X = 9  12 ,9  12
Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers
in terms of i. use a comma to separate answers as needed.
What are the approximate solutions? x  5.536, 12.464
Use a comma to separate answers as needed. Round to the nearest thousandth as needed.
11) Find the vertex the line of symmetry, and the maximum or minimum value of f(x). Graph the
function. f ( x)  7  x 2
The vertex is (0, 7)
What is the equation of the line of symmetry x = 0
What is the maximum/minimum of f(x)? 7 (maximum)
Is the value of f(0)=7 a minimum or maximum? maximum
10
y
8
6
4
2
x
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
-4
-6
-8
-10
12a) solve 5 x 2  10 What are the solutions?  2 , 2


12b) find the x-intercepts of f ( x)  5x 2  10 What are the x- intercepts?  2 ,0 ,
13) Solve by completing the square x 2  3 x  4  0 the solution is x = -4,1
2 ,0

14) Find the vertex the line of symmetry, and the maximum or minimum value of the quadratic function.
Graph the function. f ( x)  2 x 2  12 x  2
The vertex is (3, -16)
What is the equation of the line of symmetry x = 3
What is the maximum/minimum of f(x) -16
Is the value of f(3)=-16 a minimum or maximum? minimum
20
y
15
10
5
x
0
-20
-15
-10
-5
0
5
10
15
20
-5
-10
-15
-20
16) find and label the vertex and the line of symmetry. Graph the function. f ( x )  
The vertex is (0, 0)
The equation of the line of symmetry is x = 0
What graph would represent f(x)?
1 2
x
2
10
y
8
6
4
2
x
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
-4
-6
-8
-10
17) find and label the vertex and the line of symmetry. Graph the function. f ( x)  2( x  1) 2
The vertex is (-1, 0)
The equation of the line of symmetry is x = 0
What graph would represent f(x)?
10
y
8
6
4
2
x
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
-4
-6
-8
-10
18) A student opens a mathematics book to two facing pages. The product of the page numbers is 1980.
Find the page numbers.
The first page is 44
The second page is 45
19) The width of a rectangle is 1ft less than the length. The area is 2 ft 2 . Find the length and the width.
The width is 1 ft
The length is 2 ft
20) solve for x x 2  6 x  4  0
X =  3  5 ,3  5
21) solve the formula for the given number. Assume all variables represent non-negative numbers.
E  mc 2
Choose the correct value for c from the possibilities.
a) c 
e
m
22) Graph the function. Find the vertex, line of symmetry, and maximum or minimum value.
f ( x)  ( x  2) 2 1
The vertex is (-2, -1)
The minimum value of f(x) = -1
How would this be graphed?
10
y
8
6
4
2
x
0
-10
-8
-6
-4
-2
0
-2
-4
-6
-8
-10
23) Find the x- and y-intercepts
2
4
6
8
10
f ( x)  4 x 2  20 x  25
The y-intercept is (0, 25)
 5 
,0 
 2 
The x-intercept is  