alg II Hp final review guide

alg ii hp-
There will be 15 problems:  4 from radicals, 4 polynomials, 2 conics, 2 quadratics and 3 from the opening chapter on parent functions and transformations.
No matter what chapter, finding solutions and determining reasonable solutions are the top skills being assessed.




Name ___________________________   period _________  final review guide

1.         If G(x) = 2x² + 3x -8, then G(-3) =

2.         If f(x) has point (-3, 0) on it, what will the coordinates of the transformed point be if: a. g(x) = 4f(x)   b.   h(x) = f(2x)  c.  m(x)= f(x+1) – 5

3.         If f(x) = x², then describe all transformations that happen to make

g(x) = -2(x-3)² -9

4.         Describe the solutions to the equation f(x) = 5x² + 19x -1

5.         Solve 5 + 2x² = 12x then write the domain and range

7.         If 4- 3i and 4 + 3i are the roots, what is the equation?

8.         Simplify i³³

9.         Simplify i³⁰¹

10.  Spiderman jumps from the top of a building to a ledge that is 22 feet off the ground.  His height during the fall is shown by the model g(t) = -16t² + 18 with t standing as time.  At how much time after his jump will he arrive at the ledge?

11. A hunter shoots a dart through a blowgun.  The dart travels by M(t) = – 5t² + 10t + 2 where M(t) is height and t is time in seconds.  He is trying to hit a wild turkey that is in a tree that is 4 meters off the ground.  Will the dart hit the turkey?  Explain your reasoning.

12. What is the maximum height the dart can reach?

13.   Simplify these rational expressions- 
---these disappeared when I pasted them in, however I can describe the problems.  You will have fractions with radicals in the denominator -  such as "1+ SR of 2"  or "7i."  you will have to multiply the numer. and demon. by the same value. That value should cancel out the radicals. 

(a)

(b)

                                   

15. Solve by factoring:  2x³ + 3x² -8x -12 = 0

16. Write a polynomial with zeros at:

a.         1, -1, 4

b.         -3, 1/2, 1/3

c.         2i, 0 and the square root of 7

17. Write and equation for a graph with root at -3, 1, 4; a y intercept at 12.

18. Draw a graph with root at -1/2, 1, 2; a y intercept at -1.

19. Draw a graph with root at -3, 2 and a double root at 5; and negative even end behavior.

20. Write the new function to f(x) = x³ + 5x² + x-8  if it is transformed by:

a.         a horizontal reflection and a vertical translation of +6

b.         a vertical stretch of 1/3

21.  Write the equation of an ellipse if the coordinates of the foci are and  and the length of the major axis is 20. (Hint: Sketch a picture)

22.  Graph:  4(x – 2)² + 16(y+3)²  = 64                              

23.   Put in standard form and graph:   x² + y² -6x -8y + 15 =0

24.  Graph:  y + 1 = -(x-2)²

25.  Write an equation for the asymptotes for a hyperbola with a h,k of (2, 1) and a=5 and b=3.

26.  Solve:    the square root of (x+4) = x – 8.

27. Solve:   -2 times the cube root of (5x-5)= -10.

28.  Solve:  the square root of (x2+3x+6) - the square root of (x2+3x-1) = 1

29.  Barbi makes Ken a box to hold his mustache collection, which is vast.  She starts with a piece of cardboard that is 14 by 11 inches, cutting out x from each corner and folding it into a box.  What is the maximum volume she can create for this box?

34. Solve:  2x³ + 3x² -8x -12 = 0

35. If f(x) has point (–3, 0) on it, what will the coordinates of the transformed point be if: a. g(x) = 4f(x)   b.   h(x) = f(2x)  c.  m(x)= f(x+1) – 5