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

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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)

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[pic]

5a) [pic] b) [pic]

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