Algebra 2 - Review

Factoring / Solving Quadratics

100

Factor the following: x²-x-20

(x-5)(x+4)

200

Factor the following: 28p³-24p²

4p²(7p-6)

300

Factor the following: 7n²+32n-15

(7n-3)(n+5)

400

Solve the following quadratic: v²-6v+8=0

v={4, 2}

500

Solve the following: 5x²=-2+11x

x={1/5, 2}

Try These!

100

Write the equation of a quadratic in vertex form that has the following transformations: 

 - Shifted up 2, reflected over the x-axis 

 y=-x^2 +2 

200

Write the equation of a quadratic in vertex form that has the following transformations: 

 - Translated 3 units right, translated 4 down

y=(x-3)^2 -4

300

Factor: -2x⁴ + x³ + 18x² - 9

-x(x + 3)(x - 3)(2x - 1)

400

If f(x) = (x - 3)² and g(x) = (x + 3)² , what is          f(x) - g(x) ?

-12x

500

What is the total number of points of intersection for the graphs of y = e^x and xy = 20? 

Answer : 1

Quadratic Systems

100

Solve the following quadratic system: 

y=x²+3x-5 

y=x+3

(-4, -1)

(2, 5)

200

Solve the following quadratic system: 

y=x²-4x+6

y=x+2

(4, 6)

(1, 3)

300

Solve the following quadratic system: 

y=x²+6x-5 

y=3x-7

(-2, -13)

(-1, -10)

400

Solve the following quadratic system: 

y=x²-8x-20 

y=4x+8

(14, 64) 

(-2, 0)

500

Solve the following quadratic system: 

y=x²-10x+14

y=7x-16

(15, 89)

(2, -2)

Take a Chance!

100

The solution to the equation: 

5e^x+2 = 7

-2 + ln(7/5)

200

Does x² - 4x + 13 = 0 have imaginary solutions? Justify. 

Yes: sqrt -36 is imaginary

300

If cube root 81x¹⁵y⁹ = 3^ax⁵y³, what is the value of a?

a = 4/3     (81 = 3⁴⁾

400

Multiply the following: 

(2x^2 +5x+2)(2x-1)

4x^3+8x^2 -x-2

500

Find the solutions to the following system: 

x² + y² = 25

y + 5 = 2x

(0, - 5) and (4, 3) 

Radicals

100

Simplify 

sqrt(80)

4sqrt(5)

200

Simplify:

∛54a^-6

(3*∛2)/a^2

300

Simplify: 

(sqrt(16a^7))/(∛(8a^3) 

2a^2 *sqrt(a

400

Simplify:

∛(2/(3x))

 (∛18x^2)/(3x) 

500

Simplify: 

(3+sqrt(5))/(1-sqrt(5)

-2-sqrt(5)