Quadratics

Adding/Subtracting/ Multiplying

100

Add the polynomials:

(x² + 4x - 3) + (2x² - 2x + 5)

3x² + 2x + 2

200

Add the polynomials:

(2x² - 5x - 3) + (x² - 4x - 5)

3x² - 9x - 8

300

Subtract the polynomials:

(2x² - 5x + 5) - (x² + 4x - 9)

x² - 9x + 14

400

Multiply:

(x - 4)(2x + 10)

2x² + 2x - 40

500

Multiply:

2x³ (3x² + 4x - 5)

6x⁵ + 8x⁴ - 10x³

Features from an Equation

100

Are the quadratics concave up or down?

f(x) = (x-3)² - 4

g(x) = -2x² + 4x - 3

f(x) is concave up

g(x) is concave down

200

Identify the y-intercept of the function:

f(x) = x² + 4x - 5

(0, -5)

300

Identify the x-intercepts of the function:

g(x) = (x-3) (x+5)

(3, 0) and (-5, 0)

400

Identify the vertex of the function:

h(x) = (x - 5)² + 7

(5, 7)

500

What is the x coordinate of the vertex of the function?

j(x) = (x - 4) (x - 6)

The x-coordinate of the vertex is 5 (halfway between 4 and 6)

Solving by Factoring

100

Solve by factoring:

x² + 7x + 10 = 0

x=-2, x=-5

200

Solve by factoring:

x² + 20x + 9 = 0

x=-4, x=-5

300

Solve by factoring:

x² + 3x - 28 = 0

x=-7, x=4

400

Solve by factoring:

x² - 7x + 12 = 0

x=3, x=4

500

Solve by factoring:

x² - 12x + 35 = 0

x=5, x=7

Solving with Square Roots

100

Solve using square roots:

x² - 49 = 0

x=7, x=-7

200

2x² - 40 = 10

x=5, x=-5

300

-3x² + 48 = 0

x=4, x=-4

400

(x - 4)² + 8 = 44

x=10, x=-2

500

5(x - 1)² - 75 = 50

x=6, x=-4

Solving with Quadratic Formula

100

Identify A, B, and C:

x² + 4x - 1 = 0

A=1, B=4, C=-1

200

Solve using the quadratic formula:

x² - 4x - 1 = 0

x=4.236, x=-0.236

300

Solve using the quadratic formula:

x² - 7x + 12 = 0

x=4, x=3

400

Solve using the quadratic formula:

x² - 5x - 21 = 0

x=7.72, x=-2.72

500

Solve using the quadratic formula:

-3x² - 4x + 2 = 0

x=-1.721, x=0.387