Algebra 2 Review

Quadratics

100

What are the values of a, b, and c?

x² - 58= 12x

a = 1

b = -12

c = -58

200

Find the roots:

x² - x = 6

x = -2, 3

300

What are the x-intercepts of the graph of the following function?

y = 12x² + x - 20

x = 5/4, x = -4/3 

400

What is the vertex of the quadratic?

x² - 6x + 7

Vertex = (3, -2)

500

Find the solutions:

6x² - 5 = 3x

3± √ 129

     12

Logarithms

100

Rewrite the following equation in terms of log:

x⁷=254

log_x254 = 7

200

5^x=125

x = 3

300

Rewrite the following logarithmic equation in terms of exponents:

log₃81 = y

3^y=81

400

5e^x=20

x = 1.386

500

2⋅10^-4x = 200

x = -0.5

Radical/Rational

100

Solve for x:

√x=-9

81

200

What is the vertical asymptote of the given equation:

x² - x - 6

x² + x -2

X = 1

300

-2 + 6√x = 64

x = 121

400

What is the horizontal asymptote of the given equation:

    x + 5    

x² - 3x +4

Y = 0

500

Solve for x:

  2x   = 1

x² +1   x

x = -1, 1

Polynomials

100

Classify the polynomial by degree and terms:

x³ - x² + 8

Cubic trinomial

200

Is (x - 3) a factor of the polynomial x³ - 2x² + 5x - 7 

Remainder: 17

NO, (x-3) is NOT a factor

300

On which interval is 2(x - 5)² + 3 increasing?

(You may use desmos graphing)

(5, ∞)

400

What is the domain of y = x³ - 5x + 13?

(You may use desmos graphing)

All real numbers

500

Factor:

x³ - 3x² + 4x - 12

(x² + 4)(x - 3)

Random Topics

100

Will these expressions SOMETIMES, ALWAYS, or NEVER be equal?

(x+y)² = x² + 2xy + y² + 3

NEVER

200

What is the seventh term in the sequence?

16, 13.5, 11, 8.5...

1

300

What is the coefficient of the complex part of the following complex number:

-5i + 7 -17 + i

b = -4

400

Simplify: 

f(x) = 2(x+3)² - 1

2x²+12x+17

500

Write the quadratic equation from memory

-b± √b²-4ac

       2a