Solving Quadratics

Solving by Completing the Square

100

Find the missing value to complete these squares:

x²+10x+____=0

x²+12x+____=0

x²+___+4=0

25

36

4x

200

Solve by completing the square:

x²+14x-17=0

x = -7±√(66)

x=-15.12, x=1.12

300

Solve by Completing the Square:

x²+4x-32=0

x = -2 ± 6

x=4, x=-8

400

Solve by Completing the Square

x²-8x-32=0

x = 4 ± √(48)

x=-2.93,  x=10.93

500

Solve by Completing the Square:

5x²+30x+10=0

x=-5.64, x= -0.35

Solving by Factoring

100

Solve by Factoring:

x²+13x+40=0

[Include the Factors and Solutions in your answer!]

(x+5)(x+8)=0

x=-5, x=-8

200

Solve by Factoring:

x²-9x-36=0

[Include the Factors and Solutions in your answer!]

(x-12)(x+3)=0

x=12, x=-3

300

Solve by Factoring:

7x²+9x+2=0

[Include the Factors and Solutions in your answer!]

(7x+2)(x+1)=0

x=-2/7, x=-1

400

Solve by Factoring:

3x²+5x-50

[Include the Factors and Solutions in your answer!]

(3x-10)(x+5)=0

x=10/3, x=-5

500

Solve by Factoring:

6x²+61x+10=0

[Include the Factors and Solutions in your answer!]

(6x+1)(x+10)=0

x=-1/6, x=-10

Adding, Subtracting, and Multiplying Polynomials

100

Add the two trinomials:

(5x²-6x+3)+(6-7x³+4x²)

[Write your answer in standard form!]

-7x³+9x²-6x+9

200

Subtract the two trinomials:

(4x-6x³+7)-(4+2x+4x³)

[Write your answer in Standard Form!]

-10x³+2x+3

300

Subtract the two trinomials:

(3x³+4x²-6x)-(5x²+2x+4x³)

[Write your answer in Standard Form!]

-x³-x²-8x

400

Multiply the following binomial pairs:

1. (-4x+8)(8x+7)

2. (-7x²+7)(4x-8)

[Write your answers in standard form!]

1. -32x²+36x+56

2. -28x³+56x²+28x-56

500

Complete the following operations:

(10x²+24x+42) - (4x+8)(-5x-3)

[Write your answers in standard form!]

30x²+76x+66

Zero Product Property

100

Solve BOTH equations for x:

1. (x+6)(x-2)=0

2. (x+972)(x-273)=0

1. x=-6, x=2

2. x=-972, x=273

200

Solve BOTH equations for x:

1. (x+4)(x-7)=0

2. (x+10)(x-13)=0

1. x=-4, x=7

2. x=-10, x=13

300

Solve BOTH equations for x:

1. (2x+5)(5x-9)=0

2. (5x+1)(3x-4)=0

1. x=-5/2, x=9/5

1. x=-1/5, x=4/3

400

Solve BOTH equations for x:

1. (3x+4)(x-3)=0

2. (7x+1)(10x-3)=0

1.  x=-4/3, x=3

2.  x=-1/7, x=3/10

500

Create a single equation with the following solutions:

 x=-3/2,   x=5

Equation:

(2x+3)(x-5)=0

Blast from the Past

100

What is the point-slope formula?

y-y₁=m(x-x₁)

200

Simplify the exponential expression:

(5x²yz⁴)³

125x⁶y³z¹²

300

Line v has a slope of –7/9. Line w is perpendicular to v. What is the slope of line w?

9/7

400

What is the formula for slope?

m=(y₂-y₁)/(x₂-x₁)

500

What is the slope of the equation 4x+5y=10?

m= -4/5