Math III Honors Unit 3 Test Review
Name: _______________________
I. Graph the Inequalities (Make a table of points as needed; Check Line Type and Shading)
 LIST the VERTEX, AXIS OF SYMMETRY,and y-intercept.
y  2( x  1)2  3
1.
2.
y  x2  4x  1
II. Finding/ Identifying elements of a quadratic (vertical and horizontal:
(A) Axis of Symmetry
(C) Direction of opening
(E) Directrix
(B) Vertex
(D) Focus
+ 5x – 11 = y
4.
x  3( y  4) 2  2
y   ( x  3) 2  5
6.
x  2 y2  3 y  7
3. 4x2
5.
III. Solving Quadratic Equation:
Give answers as EXACT VALUES! (Reduce and Rationalize all Fractions and Radicals)
7. Solve by factoring:
x  5 x  14  0
2
8. Solve by quadratic formula:
9. Solve by completing the square:
2x  5x  7  0
3x2  9x  4  0
2
Solve quadratic equation by any method of your choice
10.
x 2  4 x  10
12.
4( x  5)2  3  14
11.
13. 7 x  140  0
2
14. 5 x  12 x  11  3 x  8 x
2
3x2  8x  2x  6
2
15.  2 x  8 x  5  0
2
IV. Solving Quadratic Inequalities
 Answers should be inequality, all reals, or no solution.
1 2
x  x4 0
16.
2
17.
x 2  3 x  10  0
18.
x 2  3 x  10  x  25
19.
0  2x2  8x
20.
3x2  2x  8  2x2  7
21.
0  x2  9
V. Roots to Standard Form: Write a quadratic equation in the standard form
y  ax 2  bx  c with integer coefficients based on the given roots.
22. –6 and 2
23. 3/2 and -2/9
24. -1/3 and 5
25. 7i and - 7i
26. 2 + 2i and 2 - 2i
27. 3 + 5i and 3 - 5i
VI. VERTEX FORM: Vertical: y  a( x  h)  k Horizontal: x  a( y  k )  h
Based on the given information, find the vertex form equation of a parabola
2
2
28.
x = y2 – 6y + 2
29.
y = -x2 + 5x – 2
30. y
= 2x2 + 4x – 9
31. x
= -3y2 + 9y + 5
32. Vertical parabola with vertex (- 3, 7) that
passes through (4, -3).
34.
vertex: (3, -5)
Focus: (3, -6.25)
35.
33. Horizontal parabola with vertex (-2, 5)
that passes through (6, 7).
vertex: (7, -4)
directrix: x=4.5
36.
directrix: y = 8
focus = (-3, 2)
VII. COMPLEX NUMBERS: SIMPLIFY each expression completely
37. ( 3i  4)( 5  i )
38. (7  9i )  3(5  2i )  i ( 3i  4)
2
39. ( 3i )( 5i )
40.
41. ( 2i )( 8i )( 9i )
 42   30
5
5  3i
42.
8i
43.
44. Solve for x and y:
45. Solve for m and n:
4 x  5  8i  17  2 yi
8
7
2  3i
3  4i
 11  3ni  i  4m  n  10i
VIII. Quadratic Transformations: Describe the changes to x and y based on f(x) = x2
46. f(x + 3) – 7
48. f(2x) + 7
47. 3(x – 4)2 + 5
49. - (2x)2 – 3
WORD PROBLEM EXAMPLE:
50. The height of a rocket shot into the air is modeled by the equation
where h is the height in meters of the rocket after t seconds.
a. Find the maximum height of the rocket and when it occurs.
b. When does the rocket return to the earth?
h( t )  16t 2  60t ,