Download Quiz 8

Math 99
Quiz 8
11/20/07
Name: __________________________
+_____
60
Write your name bigger on the back. If you need scratch paper, please ask me. For full credit, show
all work as discussed in class. Use algebra to solve the following problems. Also, express your
solutions with fractions only (no decimals).
1. Given the function f ( x)  x 2 , match the correct transformation of this function to an equation
below. Place the letter of the transformation next to the correct equation. (Note: Two
transformations will not be used.)
A. Vertical shift up
2
y  ( x  10)
B. Vertical shift down
2
y  x
C. Horizontal shift right
y  x2  6
y  ( x  3)
D. Horizontal shift left
2
E. Narrower than f ( x)  x
2
2
F. Wider than f ( x)  x
G. Opens down
y  x2  4
2. Consider f ( x)  ax 2  bx  c . Choose the description that best describes each graph shown
below. Choose A, B, C, or D.
Choices:
A) a > 0
b<0
c>0
y
B) a > 0
b=0
c<0
C) a < 0
b=0
c>0
x
i. ___________
ii.
iii.
x
x
ii. ___________
iii. ___________
3. Given the horizontal parabola x  ( y  2) 2  3 , the circle the correct letter choice for the
coordinates of the vertex:
a. (3,2)
b. (-3,2)
_____
6pts
D) a = 0
b>0
c<0
y
y
i.
Choices:
_____
5pts
c. (-3,-2)
_____
4pts
d. (3,-2)
/15 points
4. Using the discriminant, decide how many x-intercepts the graph of each equation has.
Circle your choice.
a. y  x 2  2 x  3
Two
One
Zero
b. y   x 2  5 x  1
5. Solve b 
Two
One
_____
3pts
_____
3pts
Zero
R2k
for R. Simplify your answer.
ak 2
R = ___________________
_____
4pts
x = ___________________
_____
4pts
6. Solve 4 x  hx  m for x. Simplify your answer.
2
7. Carefully graph y  x 2  2 x  3 . Show your algebraic work to get the vertex and x-intercepts.
Label the key points you find below with their ( x, y ) coordinates as well as the line of
symmetry.
y
a. The vertex
b. Line of symmetry
c. The y-intercept
d. The point symmetric to the y-intercept
e. Any x-intercepts
_____
12pts
x
/26 points
8. A cliff diver has just jumped from a cliff and will soon splash into the water below. The diver’s
height above water is given by h  16t 2  12t  40 where h is in feet and t is time in seconds
since the diver jumped. Solve algebraically when necessary and include units with your answer.
a. How high is the cliff?
__________________________
_____
3 pts
__________________________
_____
4 pts
b. When does she hit the water?
9. A uniform border of bark chips is to be placed around three sides of a 20 foot by 20 foot square
garden. How wide should the border be, given that you only have enough bark to cover 62
square feet of area? Define your variable (or label the picture with your variable),
solve algebraically, and give an exact answer (no decimals) with units.
__________________________
_____
6 pts
10. Find a pair of numbers whose sum is 50 and whose product is a maximum. Show all work
algebraically to receive full credit. (Hint: Let x and 50-x represent the two numbers.)
x = __________
50-x = __________
_____
6 pts
/19 points