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Characteristics of Quadratics

100

Find the Axis of Symmetry:

4x² - 16x + 10

2

200

Find the Axis of Symmetry & Vertex:

-3x² + 12x - 10

Axis of Symmetry: 2

Vertex: (2, 2)

300

Find the Axis of Symmetry:

3x² - 6x + 15

1

400

Find the Vertex:

y = x² + 12x + 45

(-6, 9)

500

Find the Vertex:

y = -x² - 8x - 20

(-4, -4)

Add & Subtract Polynomials

100

Add the Polynomials: 

(5x + 3) + (3x + 5)

8x + 8

200

Subtract the Polynomials:

(3v - 23) - (21v - 2)

(-18v - 21)

300

Add the Polynomials:

(5p² - 3) + (2p² - 3p³)

-3p³ + 7p² - 3

400

Add the Polynomials:

(-x⁴ + 13x⁵ + 6x³) + (6x³ + 5x⁵ + 7x⁴)

18x⁵ + 5x⁴ + 12x³

500

Subtract the Polynomials:

(3a² + 4b² + 3c + 5b² + 3c² + 7abc) + (3ab + 3c² + 4c) + (3a² + 3c²)

(7abc + 3ab + 6a² + 9b² + 9c² + 7c)

Multiplying Polynomials

100

Multiply the Polynomials:

(x - 2) (3x - 9)

3x² - 15x + 18

200

Multiply the Polynomials:

(5x - 10) (12x + 3)

60x² - 105x - 30

300

Multiply the Polynomials:

(2x² + 5x + 2) (8x + 1)

16x³ + 42x² + 21x + 2

400

Square the Polynomial:

(2x + 2)²

4x² + 8x + 4

500

Multiply the Polynomials:

(5x⁵ + 2x⁴ + 12x³ + 4x² +3x - 2) (8x⁵ + 6x⁴ + 12x³ + 6x² + 5x - 1)

(80x⁸ + 40x⁷ - 74x⁶ + 51x⁵ + 14x⁴ - 84x³ - 52x² - 27x + 18)

Quadratic Formula & Discriminant

100

Find the Discriminant:

 x² + 6x + 3

24

200

Solve using the Quadratic Formula:

x² − x = 6

(3, -2)

300

Find the Discriminant:

6x² + 12x + 87

-1944

400

Solve using the Quadratic Formula:

2x² + 2x − 7 = 0

(-1 + (the square root of 15))/2

(-1 + (the square root of -15))/2

500

Find the Discriminant:

63x² + 45678x +58

2086465068

Factoring & Completing the Square

100

Factor completely: 

8x + 4

4(2x + 1)

200

Solve the Equation by Completing the Square:

a² + 14a - 51 = 0

(3, -17)

300

Solve the Equation by Completing the Square:

n² - 3n - 3 = 0

(3, -1)

400

Factor Completely:

x² + 7x +10

(x + 5) (x + 2)

500

Complete the Equation by Completing the Square:

3x² = -4 + 8x

(2, 2/3)