Algebra 2

Linear Functions

100

3x+5=17

x=4

200

4(x-2)+7= 3x+12

x=13

300

Find the slope of the line passing through:

(2,5) and (6,13)

m=2

400

Write the equation of the line with slope 3 passing through (2,-1)

y= 3x - 7

500

Solve the system:

{2x+y=7

{3x−2y=4

(x,y)=(2,3)

Quadratic Functions

100

Factor:

x2+7x+12

(x+3)(x+4)

200

Solve:

x2−9x+20=0

x=4,5

300

Use the quadratic formula to solve:

2x2+3x−5=0

x=1,−25

400

Find the vertex and axis of symmetry of:

y=x2−8x+11

Vertex (4,−5), axis x=4

500

A ball is launched upward from a platform. Its height is modeled by:

h(t)=−16t2+64t+80

Maximum height 144 feet

Polynomials

100

Simplify:

(3x2+4x−1)+(2x2−5x+7)

5x2−x+6

200

Multiply:

(x+3)(x−5)

x2−2x−15

300

Factor completely:

x3−4x2−12x

x(x−6)(x+2)

400

Divide:

x3+2x2−5x+6x+3\x+3

Quotient x2−x−2, remainder 12

500

Use the Remainder Theorem to find the remainder when:

f(x)=2x3−5x2+x+7

is divided by (x−2)(x-2)(x−2).

Remainder 5

Exponential & Logarithmic Functions

100

Evaluate:

2 ^4

16

200

Solve:

3^x=81

X=4

300

Evaluate:

log⁡10(1000)

3

400

Solve:

log⁡2(x)+log⁡2(x−2)=3

4

500

A population starts at 500 and grows by 8% each year.

Write an exponential model and find the population after 10 years.

P(t)=500(1.08)t, P(10)≈1079

Radical & Rational Functions

100

square root 72

6 square root2

200

Solve:

square root x+4=6

x=32

300

Simplify:

x2−9/x2+3x

x-3/x

400

Solve:

2/x + 3/x-1

x=2/5

500

Solve and identify any extraneous solutions:

Square root x+6=x−2

x=6 (valid), x=−1 (extraneous)