Algebra 2 - State College Area School District
DYR #3 Precalc Name_______________________________
Alg 2 Chapter 6 (old 9 ½ ) DO YOU REMEMBER??
1) Define:
a) determinant (of a matrix): (4.3)
b) discriminant: (5.4)
2) Write a linear system that represents the following. (3.3)
Solve the system and answer the questions.
Puff Daddy went to the store and bought 3 CDs & 2 movies for $49.
The next week he bought 2 CDs & 4 movies for $70.
How much did each CD cost? ________ How much did each movie cost? ________
3) Sketch the graph of the system of linear inequalities. (3.4)
y > 0
x+ y < 5
x>1
4) Use a determinant to find the area of the triangle with the following vertices. (4.3)
a) (-3,5) (3,-5) (2,6) b) (0,1) (2,2) (4,3)
Why did you get a strange answer?
5) Find the inverse of the matrices below (if possible). Do (a) by hand & (b) with a calc.
a) [pic] b) [pic] (4.4)
DYR3
6) Use a graphing calculator to solve the system of linear equations. (4.5)
4x – y + z = 18
2x + 2y + 3z = 19
5x – 2y - 2z = 2
7) Find the discriminant and determine the number of real solutions. (5.4)
[pic] = 0
8) Find the inverse of the function: (6.3)
f(x) = [pic]
9) Simplify Completely:
a) [pic] b) [pic] c) [pic] (7.4)
10) Solve for x: [pic] = 22 (7.5)
ANSWERS
1) det: matrix math det: dis: b2-4ac 2) $7 for a CD $14 for a movie 3)
4a) 28 4b) 0, because the sides do not form a (.
6) (2,-3,7) 7) 0, 1 8) y = [pic] 9a) [pic] 9b) [pic] 9c) [pic] 10) x = 5
DYR3
11. Simplify each expression as much as possible. Remember to rationalize the denominator if necessary.
a. [pic] b. [pic] c. [pic]
d. [pic] e. [pic]
12. Evaluate [pic] for the following values of x:
a. x = -2; f(x) = _____ b. x = 1.3; f(x) = _____ c. x = -2.3; f(x) = _____
13 If f(x) = x2 -2 and g(x) = x + 2, find each of the following:
a. (f(g)(x) b. (g(f)(x) c. (f-g)(x)
d. (f(g)(-2) e. (g(f)(4) f. (fg)(2)
14 Find the equation for a parabola that has vertex (-3, 5) and passes through the point (2, -8).
_________________________
DYR3
15 Sketch the graph: y = 2x2(x-a)3(x-b)(x-c)4. Show work for end behavior, zeros, and testing regions/multiplicity.
a b c
16 Write the equation for a polynomial with zeros (4, 3 - i, 3 + i
_________________________
17 Sketch the graph of the function: [pic]
Hole: _______ Slant A: _______
Vert A: _______ x-int: _______
Horiz A: _______ y-int: _______
ANSWERS: 11a) [pic] 11b) [pic] 11c) [pic] 11d) [pic]
11e) [pic] 12a) -6 12b) 3 12c) -7 13a) x2+4x+2 13b) x2 13c) x2–x-4
13d) -2 13e) 16 13f) 8 14) [pic] 16) x4-6x3-6x2+96x-160
17) hole x=2; HA: y=1; VA: x=4; SA: none; x-int (-2,0) y-int (0,-½)
15)
-----------------------
[pic]
5a) [pic] b) [pic]
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