Chapter P Jeopardy

Factoring

100

Factor: x² - 3x - 28

(x-7)(x+4)

200

Factor: 7x² - 65x - 50

(7b+5)(b-10)

300

Factor: 7x³ + 71x² + 72x

x(7x+8)(x+9)

400

Factor: 4x² - 20x + 25

(2x-5)²

500

Factor: 16x² - 1

(4x + 1)(4x - 1)

Solving Quadratic Equations

100

Solve: x² - 9x = -18

x = 6, x = 3

200

Solve: 3x² = -4x + 4

x = 2/3 = 0.667, x = -2

300

Solve: x² - 12x + 31 = -4

x = 7, x = 5

400

Solve: x² - 14x - 49 = 9

x = 7 - sqrt(107), x = 7 + sqrt(107)

500

Solve: x² = 5x + 5

x= (5 + 3sqrt(5))/2

x= (5 - 3sqrt(5))/2

Absolute Value Equations

100

Solve: |x - 6| = 7

x = 13, x = -1

200

Solve: 4 + |3a| = 10

x = 2, x = -2

300

Solve: |4x - 8| + 1 = 5x

x = 1

REJECT x = -7

400

Solve: |3x - 1| -1 = 4x

x = -2

REJECT x = 0

500

Solve: |3x - 3| + 9 = x

NO SOLUTIONS

reject x = -3 and x = 3

Piecewise Functions

100

find f(-1) if f(x) = 

-(x + 6)² + 1 when x < -3

-5                 when x = -3

2x                 when -3 < x </= 2

-2

200

Find f(-2) when f(x) = 

-x + 3              when x</= -3

-3x - 4             when -3 < x </= 1

-(x - 2)² + 5     when x > 1

2

300

Graph the function:

f(x) = (x + 5)² + 3      when x < -3

          sqrt(x)              when x > 0

Quadratic (open dot @ -3)

Square Root graph (open dot @ 0)

400

Graph f(x) = 

-x                 when -5 </= x < 1

sqrt(x - 1)     when x >/= 1

linear graph (closed @ -5, open @ 1)

square root (closed @ 1)

500

Graph f(x) =

x        when x < -7

|x|      when x > -7

linear (open dot @ -7)

absolute value (open dot @ -7)

Miscellaneous

100

What is the quadratic formula?

x = -b +/- sqrt(b² - 4ac)/ 2a

200

What is an extraneous solution?

Values we get when solving equations that aren't really solutions to the equations. 

300

How do you find the 'magic number' when completing the square?

(b/2)²

400

Simplify: CubeRoot(135x⁶)

3x² CubeRoot (5)

500

When do you know to reject a solution when solving an absolute value equation?

When the solution does not give a balanced equation.