1. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the
function.
f(x)= ¼(x+6)^2+6
Vertex is (-6,6)
The line of symmetry is x= -6
What is the maximum / minimum value of f(x)? 6
Is the value, f(-6)=6, a minimum or maximum? Minimum
2. Give exact and approximate solutions to three decimal places.
(x-10)^2=18
What are the exact solutions?
x= 10-3√2, 10+3√2,
What are the approximate solutions?
x= 5.757, 14.243
3. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function
and graph the function.
F(x) =x^2-8x-1
What is the vertex (4,-17)
What is the equation of the line of symmetry is x=4
What is the maximum / minimum value of f(x)? -17
Is the value, f (4) =-17 a minimum or maximum? minimum
Graph
4. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function
and graph the function
F(x)=9-x^2
What is the vertex (0,9)
What is the equation of the line of symmetry is x=0
What is the maximum / minimum value of f(x)? 9
Is the value, f (0) =9 a minimum or maximum? maximum
Graph
5. a) Solve 3x^2-7x-11=0
What are the solutions?
7 + 181 7 − 181
,
6
6
 7 + 181   7 − 181 
,0 , 
,0 

6
6



b) Find the x-intercepts of f(x)= 3x^2-7x-11 
6. Solve the formula for the given letter. Assume all variables represent nonnegative numbers.
A^2+1^2=f^2, for a
a=
f 2 −l2
7. Give exact and approximate solutions to three decimal places.
X^2+2x+1=4
Exact: 1,-3
8.
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 60ft of fence? What
should the dimensions of the garden be to give this area?
The maximum area that the farmer can enclose with 60 ft of fence is __450____ sq ft.
The dimension of the garden to give this area is 30 ft by __15____ ft.
9. Solve by completing the square.
X^2+13/2x=13; what is the solution?
Answer:
− 13 + 377 − 13 − 377
,
4
4
10. A student opens a mathematics book to two facing pages. The product of the page number is
1482. Find the page numbers.
The first page is ___38____
The second page is __39______
11. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the
function.
F(x) = -(x+1) ^2-5
The vertex is (-1,-5)
The line of symmetry is x= -1
The maximum/minimum value of f(x) is -5
The value, f (-1) =-5, is maximum
Graph
12. Find the vertex, the line of symmetry, and the maximum or minimum value of the quadratic
function, and graph the function.
F(x)=-2x^2+2x+3
The x-coordinate of the vertex is ___1/2___
The y coordinate of the vertex is ____7/2___
The equation of the line of symmetry is x =1/2
The maximum / minimum of f(x) is 7/2
The value, f(1/2) =7/2 is ? maximum
13. Write a quadratic equation in the variable x having the given numbers as solutions. Type the
equation in standard form, ax^2+bx+c=
Solution: 7, only solution
The equation is x^2-14x+49 =0
14. Solve for x
X^2-x+4=0
Answer:
1 + 15 i 1 − 15 i
,
2
2
15. Find and label the vertex and the line of symmetry. Graph the function.
F(x)=4x^2
Vertex = (0,0)
Line: x=0
16. The length of a rectangle is twice the width. The area is 8yd^2. Find the length and the width.
Width = 2, lengt = 4
17. Find the x-and y-intercepts
F(x) =16x^2+8x+1
x-intercept: (-1/4,0)
y-intercept = (0,1)
18. Determine the nature of the solutions of the equation.
X^2-13=0
2 real solutions
19. Give exact and approximate solutions to three decimal places.
X^2 -5x+3=0
The exact solutions are x=
5 + 13 5 − 13
,
2
2
The approximate solutions to 3 decimals places are x= 4.303, 0.697
20. Determine the nature of the solutions of the equation.
Y^2=5/8y+4/5
2 real solutions