Algebra 2 Review

Graph Identification

100

The shape of the graph y=x²

Parabola

200

The direction of opening of x = -3(y+2)² - 5

Left

300

A type of conic section whose two foci are further from the center than its vertices

Hyperbola

400

The vertex of y=x²+10x+22

(-5, -3)

500

The center of x²+y²+20x-10y+100=0

(-10,5)

Exponents and Logs

100

The simplified form of ln(e)

1

200

The simplified form of log₃27

3

300

x when log₂8 = log₄x

64

400

The positive solution of log₆8 + log₆(3x²) = 5

18

500

The solution of log₃(x + 1) - log₃x = 2

1/8

Right Triangles

100

In a 45-45-90 triangle, the length of one leg if the other leg is 5 units long

5 units

200

The length of the hypotenuse of a 30-60-90 triangle, given that the length of the side opposite the 30 degree angle is 1 meter

2 meters

300

The tangent of either 45 degree angle in any 45-45-90 triangle

1

400

The reciprocal of cosine

Secant

500

cscθ if sinθ = (√2) / 2

√2

Solve for x

100

Both solutions of |x-2| = 2

0 and 4

200

The solution of (1 / 25)^3x+1 = 625

-1

300

The solution of e^-x - 5 = 79

(exact form)

-ln84

400

Both solutions of 4x² = -2

± (i√2) / 2

500

Both solutions (from 0 to 360) of 0 = (-1 / 5) * tanθ

0 and 180

Radical Number Sense

100

The largest of the following numbers: 1,2,√2,√3

2

200

The integers that √76 is between

8 and 9

300

The smallest of the following numbers:

(√2)/2, (√3)/3, 2, 1

(√3)/3

400

The most simplified form of √120

2√30

500

The most simplified form of (√56) / (√14)

2