SI Jeopardy

Factoring Polynomials & Rational Expressions

100

Factor the expression completely:

6x² - 15x

3x(2x - 5)

200

How can we determine which numbers to exclude from the domain of a rational function?

Set the denominator equal to 0 and solve for x

300

Solve the equation:

x² - 4x = 5

x = -1, 5

400

What numbers must be excluded from the domain of this rational function?

f(x) = (x + 3)/(x² - 5x + 6)

2, 3

500

Simplify the rational expression:

(15x² + 58x - 8)/(2x² - 32)

(15x - 2)/2(x - 4)

Radical Equations & Rational Exponents

100

When do we need to use a "plus or minus" symbol?

When we take the square root of our variable squared

200

When your exponent is a fraction, what do the numerator and denominator each represent?

Power over Root

300

Find all solutions:

2x² = 50

x = 5, -5

400

Evaluate without a calculator:

64^2/3

16

500

Find all solutions:

(x + 2)^4/3 = 81

x = -29, 25

Simplifying Square Roots & Complex Numbers

100

What is the imaginary number, i, equal to?

i = sqrt(-1)

200

Simplify the radical expression:

sqrt(45)

3 sqrt(5)

300

Subtract the complex numbers:

(-3 + 2i) - (3 - 5i)

-6 + 7i

400

Simplify the radical expression:

sqrt(-28) + sqrt(-63)

5i sqrt(7)

500

Divide the complex numbers. Be sure to rationalize your result!

(5 - i)/(2 + i)

9/5 - 7i/5

Quadratic Formula & The Discriminant

100

What is the discriminant?

The part under the square root: b² - 4ac

200

How many x-intercepts does your parabola have if the discriminant is positive?

2

300

How many x-intercepts does your parabola have if the discriminant is negative?

0

400

Solve using the Quadratic Formula:

x² + 8x = -16

x = -4

500

Solve using the Quadratic Formula:

x² = 2x - 17

x = 1 + 4i, 1 - 4i

Transformations of Functions

100

What kind of transformation is indicated by a negative sign?

Reflection or "flip"

200

What kind of transformation is indicated by addition and subtraction?

Shift

300

Use the words ' horizontal' and 'vertical' to make the following statement true:

Function transformations that appear inside the function are in the                          direction (and reversed!); transformations that appear outside the function are in the                         direction.

horizontal; vertical

400

Give the parent function and describe the transformations on the following function:

g(x) = (x + 3)³ - 8

Parent: f(x) = x³

Shifted Left 3 and Down 8

500

If the parent function, f(x), passes through the point (1, 1), find its corresponding point on the transformed function:

g(x) = -f(x - 2) - 3

(3, -4)