Algebra 2 - Quadratics Review

Find the Vertex

100

Find the vertex. y = -3(x+2)² - 10

(-2, -10)

200

Find the vertex. y=x²+10x+16

(-5, -9)

300

Find the vertex. y-5=4x²+8x-3

(-1, -2)

400

Find the vertex. y=-7x²-15x+21

(1.07, 29.04)

500

Find the vertex by completing the square:

2x²+12x+22

y=2(x+3)²+4

Factoring

100

Solve by Factoring: 0=x²+7x+12

(x+3)(x+4) ==> x = -3, -4

200

Solve by factoring. y=25x² - 36

(5x+6)(5x-6) ==> x=6/5 , -6/5

300

Solve by factoring: 3x²+10x-5=3

(3x-2)(x+4) ===>2/3, -4

400

Factor completely y=12x²-27

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

500

Solve by Factoring. 6x²-39x-45=0

3(2x-15)(x+1) ====> (x= 15/2, -1)

Completing the Square

100

Solve by completing the square. x²+6x-5=0

x= -3± √ 14 

200

Solve by completing the square. 2x²-16x+1=-1

x = 4± √ 15 

300

Convert to vertex form by completing the square. f(x)=x²-4x+13

f(x)=(x-2)²+9

400

Convert to vertex form by completing the square. f(x)=-3x²-18x-7

f(x)=-3(x-3)²+20

500

Convert to vertex form by completing the square: f(x) = 2x²-5x+8

f(x)=2(x-1.25)²+4.88

Quadratic Formula

100

Solve by the quadratic formula. x²-5x-1=0

x= (5± √ 33  )/2

200

Solve by the quadratic formula. f(x) = 2x²-6x-3=4

x= (3± √ 23  )/2

300

Solve by quadratic formula. 3x² - 2= - 5x

x= -2, 1/3

400

Solve by quadratic formula. 5k²+1=6-18k

x= (-9± √ 106  )/5

500

The roots of the following equation, x²+6x+36

x=3+3iroot(3)

x=3-3iroot(3)

Bonus

100

These two winter Olympic sports used to be in the the summer Olympics. (Name one)

Figure Skating, Ice Hokey

200

The only city to opt out of being a host city

What is Denver?

300

Prior to this years games this country has the most winter Olympic medals.

Who is Norway?

400

They year of the first Winter Olympics.

What is 1924?

500

The year the summer and winter Olympics began not being in the same year.

What is 1992?