Algebra II Checkpoint

Solving Quadratics

100

Find the x-intercepts:

y=x²+2x-15

(-5,0) and (3,0)

200

Find the x- and y- intercepts:

y=3x²-5x+2

x-intercepts: (-1/3,0) and (2,0)

y-intercept: (0,2)

300

Solve for x:

0=-4x²+8x+3

x= -0.32 and x=2.32

400

Complete the Square:

y=x²+6x-11

y=(x+3)² - 20

500

Factor the following expression:

4x² - 9

(2x+3)(2x-3)

Solve for x

100

Solve for x:

sqrt(3x+13)=x+5

x= -4 and x=-3

200

Solve for x:

3(x-2)³=81

x=5

300

Solve for x:

|3x-6|-2=19

x=9 and x=-5

400

Solve for x:

3x/5=(x-2)/4

x=-10/7

500

Solve for x

(2x+3)/6 + 1/2 = x/2

x=6

Graphing Form

100

What is the vertex of this equation?

y= 3(x-7)² + 19

vertex: (7,19)

200

Where is the locator point of this graph?  Sketch it.

y= 2(x-3)³ + 5

(3,5)

300

Where are the asymptotes of this graph?  Sketch it.

y=1/(x+3) - 4

x=-3 and y=-4

400

Sketch the graph:

y=2*sqrt(x+2) - 4

Endpoint at (-2,-4).  Stretch factor of 2.

500

Put the equation in graphing form and sketch the graph.  Label key points.

y=x²+2x-3

y=(x+1)² - 4

Vertex: (-1,4)

y-intercept: (0,-3)

Inverse Equations

100

Find the inverse:

y = 1 + sqrt(x+5)

y = (x-1)² - 5

200

Find the inverse:

y = (x+1)/4

y = 4x - 1

300

Solve for x:

log₄(2x+3) = 1/2

x = -1/2

400

Solve for x:

log₄6=x

log(6) / log(4) = 1.29

500

Solve for x

log₂144 - log₂x = log₂9

x=16

Systems of Equations

100

Solve the system:

2x + 5y = 19
y = 3x - 3 

(2,3)

200

Solve the System

3x - y = 7
2x + y = 8

(3,2)

300

Solve the system:

3x - 14y = 72
9x + 22y = 18

(9.58,-3.09)

400

Solve the System:

4x + 2y = 14
3x - 5y = -22

(1,5)

500

Solve the System:

-2x + 2y + z = 14
3x - 2y + z = -5
-x + y - 2z = -8

(-3,1,6)