PAP Algebra II Chapter 5 TEST #2 REVIEW
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1. What is the y-intercept of the following function? y  4 x  2   3
2
2. Find the S/R/Z of the following function:
f ( x)  3 x 2  5 x  2
3. Simplify the following expressions:
A.
 54
B.
5  2i  3  4i 
C.
2  4i
1  3i
4. The following quadratic is given in VERTEX FORM:
y  2 x  2   7
2
Change it to STANDARD FORM ( y  ax 2  bx  c )
5. Factor the following expressions:
A. 49 x 2  36
B. 2 x 2  7 x  15
C. 3x 2  13x  4
6. Given the quadratic function, y  2 x 2  6 x  8 Find the following:
A.
B.
C.
D.
E.
Axis of symmetry equation:
Y-value of the vertex:
Y-intercept:
Make a quick sketch of this function, by plotting the vertex, y-intercept:
Explain how the graph could tell you what type of roots you would have, real vs imaginary?
7. Given a point (2,5) and vertex
1,2 write the equation in vertex form.
8. Find the S/R/Z by factoring: 2 x 2  11x  12  0
9. Find the S/R/Z by completing the square:
x 2  6 x  41  0
10. Find the S/R/Z by using the quadratic formula:
11. The equation of a parabola in vertex form is
x 2  6 x  11  0
y   x  4   3 ( A sketch could help )
2
A. If you translate this equation left 5 and down 2, what would be the new equation?
12. A punted football can be modeled with the quadratic h  0.01x 2  1.18 x  2 . The horizontal distance
in feet from the point of impact with the kicker’s foot is (x) and (h) is the height of the ball in feet.
A. What is the exact horizontal distance when the ball is at its maximum height?
B. What is the maximum height?
13. A rectangle has a length that is 4 cm more than the width (w). Its area equal to 21 cm2 .
A. Write a quadratic function to model the above situation.
B. Solve the equation to find the dimensions of your rectangle.
14. Two scooters leave from the same point at the same time. One scooter travels due EAST and the other
scooter travels due NORTH. The scooter going NORTH travels 7 miles per hour faster than the scooter
going EAST. After one hour, the scooters are a distance of 13 miles apart.
A. Let x be the speed of the slower scooter. Write an equation that relates the speeds of the
scooters and the distance that they are apart after one hour.
B. Using the equation you have found in part (A), solve the equation and find the speed of each
scooter. Remember you are trying to find the S/R/Z???
C. Which of your roots is not an actual answer for the speed of the scooter? Explain why?
15. Find a quadratic model from data showing the price of a 1 st class postage stamp and the year of that price.
Year
Price(cents)
1974
10
1978
15
1981
18
1983
20
1988
25
1995
32
2001
34
16. h(x) = –16x2 + 175 models the height of a rock dropped from 175 feet where x is time in seconds.
Graph it : scale 10 on y and 0.25 on x
Exactly when does the rock land?
What is the height at 2 seconds?
What is a reasonable domain?
What is a reasonable range?
2002
37