Quadratics Review Game

Graphing

100

What is the formula for AOS? What relationship does the AOS and vertex have with one another?

AOS: X= -b/2a 

x coordinate of the vertex is the AOS

200

How do you determine if the parabola opens up or down?

a>0, opens up

a<0, opens down

300

Graph y=x²+6x+8. State the vertex, AOS, y-intercept, min/max value, domain, range, and roots.

vertex: (-3, -1), AOS: x=-3, y-int: (0,8), min value: -1, domain: All real numbers, range: [-1, infinity), and roots: x=-4, -2

400

Graph y<x²+8x-5

Dashed

Vertex: (-4,-21)

points: (-8, -5), (-7, -12), (-6, -17), (-5, -20), (-3, -20), (-2, -17), (-1, -12), (0,-5)

Shade outside the parabola

500

Solve x²+64 >= 16x

x²+64 >= 16x

x²-16x+64 >=0

(x-8)(x-8) = 0

All real numbers

Factoring

100

What is the first thing we need to look for before factoring?

Look for GCF (Greatest Common Factor) to pull out: what they all share (values, variables, shapes, etc).

200

Match:

1. x²-3x-10                                         A. Difference of Squares

2. 3x²+7x-20                                      B. Trinomial: a is not 1, then grouping

3. x²-81                                             C. Grouping 

4. 35x³-14x²-25x+10                          D. Trinomial: a=1                      

1. D

2. B

3. A

4. C

300

Solve x²-3x=18

x= -3, 6

400

Solve 7n²+4=-16n

n= -2/7, -2

500

Solve 9p³+58p²-35p=0

P= -7, 0, 5/9

Square Root

100

How do we solve by square root? What is key goal needed to solve by square root?

Get x² by itself or solve for x: take the square root of both sides after getting x² by itself.

200

Solve p²+8=72

p=-8, 8

300

Solve 9k²+5=167

k= +- 3 square root 2

400

Solve 3b²-9=-30

b= +- i square root 7

500

Solve 2r²-10=-37

r= +- (3i square root 6)/2

Completing the Square

100

What is the first step needed to complete the square?

Get all variables to one side of the equal sign and a=1.

200

What do we need to find to add to both sides of the equation? What is the formula to find it?

The new c value. C= (b/2)²

300

Solve x²+6x=16

x²+6x=16

x²+6x+9=16+9

(x+3)²=25

x+3 = +- 5

x= -8, 2

400

Solve n²+2n-34=0

n= +- (square root 35) - 1

500

Solve 4n²+16n-26=4

n= +- [(square root 46)/2] - 2

Discriminant/Quadratic Formula

100

What is the formula for the quadratic formula?

x= [-b +- (square root(b²-4ac)]/2a

200

What is the formula for discriminant?

D= b²-4ac

300

Match:

1. D=0                  A. Two real solutions

2. D<0                  B. No real solutions/Two imaginary solutions

3. D>0                  C. One real solution

1. C

2. B

3. A

400

Find the discriminant AND state the number and type of solutions. 

3b²-8b+4=7

D=100, two real solutions

500

Use Quadratic Formula to solve

9x²-6=2x

x= [1 +- (square root 55)]/9