Quadratics Review

Factoring a=1

100

x² + 4x + 3

(x+3)(x+1)

200

x²+ 8x - 20 

(x+10)(x-2)

300

x² - 12x + 35

(x-5)(x-7)

400

b² - 17b + 72

(b-8)(b-9)

500

n² - 2n - 63

(n-9)(n+7)

Factoring Special Case

100

a² - 9

(a-3)(a+3)

200

4x² - 81

(2x-9)(2x+9)

300

16x⁴ - 25y²

(4x² - 5y)(4x² + 5y)

400

9x⁶ - 64y⁴

(3x³-8y²)(3y³+8y²)

500

4x²y⁸ - 49z¹⁰

(2xy⁴ - 7z⁵)(2xy⁴ + 7z⁵)

GCF

100

2x³ - 16x

2x ( x² - 8)

200

3x⁴ - 18x² - 6x

3x(x³ - 6x - 2) 

300

4x² - 16x + 16

4(x² - 4x + 4)

400

6x³ + 18x² - 24x

6x(x² + 3x - 4)

500

15x⁵y² - 10x³y² + 5x²y 

5x²y(3x³y² - 2xy + 1) 

Solving

100

Solve the following algebraically. 

x² - 12x + 35 

(x-7)(x-5) 

x= 7 x= 5 

200

Solve the following by factoring. 

x² + 3x - 10 

(x+5)(x-2)

x=-5  x=2 

300

Solve a²-9a-10 algebraically. 

(a-10)(a+1) 

a =10  a=-1

400

Solve x² -11x + 24 

(x-8)(x-3)

x=8  x=3

500

algebraically solve k² - 6k - 40 

(k-10)(k+4)

k=10 k=-4

Characteristics of a Quadratic

100

State the vertex of x² + 4x - 5 

(-2,-9)

200

State the axis of symmetry for y =x² + 8x

x = -4 

300

State the roots to x² - 11x + 18

the roots are 2 and 9

400

Solve for the axis of symmetry algebraically. 

y = 3x² + 12x + 5 

x = -b/2a 

x = - (12) / 2(3) 

x = -2

500

Solve the axis of symmetry algebraically for

 y = -2x² - 12x -3 

x = -b/2a 

x = -(-12)/2(-2) 

x = -3