Exponentially Entertaining Equations!

Quadratic Functions

100

What is the quadratic formula?

-b +- sqrt(b² - 4ac)       /           2a

200

Find the x-intercepts by factoring: 2x² - 8x + 6

X = {1, 3}

300

Find the x-intercepts by factoring: 5x² - 31

X =  Approximately: {-2.5, 2.5}

400

Find the x-intercepts by factoring: 6x² + 15x

X = {-2.5, 0}

500

Convert this equation into vertex form: 7x² - 8x + 1 

y = 7(x - .25)² + .75

Quadratic Transformations

100

Describe the transformation:

f(x + 5) - 9

Left 5, down 9

200

Describe the transformation:

f(-x - 1) - 1

Reflection across the y-axis, Right 1, Down 1

300

3 * f(x) - 1

Vertically Stretch by 3, Down 1

400

-f(3x + 1) - 90

Reflection across the x-axis, Horizontal Compression of 3, Left 1, Down 90

500

-9 * f(-9x + 90) + 90

Vertical Stretch by 81, Right 90, Up 90

Polynomials

100

x + 2x + x²

3x + x²

200

(2x + x²) + (-x + 2x²)

x + 3x²

300

(-9x + x³ + 8x²) + (9x + -x³ - 7x²)

x²

400

(2x - 2z) * (-x - 2y)

-2x - 4xy + 2xz + 4zy

500

((2a - 2b) * (5c - d)) / 2c

5a - (ad/c) - 5b + (bd/c)

Laws of Exponents

100

x³ * x⁰

x³

200

x8 * (x²/x⁶)

x⁴

300

((x^-9 * x⁵) / x^-18) * x^-2

x¹²

400

(x^-3 * (x⁶)²)  /  (x^-9 * x²)

x¹⁶

500

x^-3 / x^{(x^-7/x^-7)^2}   *   x^-6

1/x¹⁰

Simplifying Radicals

100

sqrt(50)

5 * sqrt(2)

200

sqrt(198)

3 * sqrt(22)

300

sqrt(156)

2 * sqrt(39)

400

sqrt(1552)

4 * sqrt(97)

500

sqrt(1552) * sqrt(425)

20 * sqrt(1649)