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LinearFunctions

Systems&

SimplifyingQuadratics Polynomials

REDDY’S ALGEBRA 2 JEOPARDY – Units 1 - 4

What is the slope of a linethrough the points

A(3, -1) and B(-17, 9)?

m = - 1/2

What are the intercepts of the line

-12x = -60 - 4y?

x-intercept: (5, 0)

y-intercept: (0, -15)

What is the inverse of the function

€

f (x) =2

7x − 5?

€

f −1(x) =7

2x +

35

2

Graph.

€

f (x) =x

4−1 +1

Simplify, expressing your answer as a fraction.

€

13

+35

34

− 4

€

−56

195

Simplify

€

(5i14 − 2)(6i)3( −1)−2

€

−1512i

Matrix A is below. Find A-1

€

A =4 3

−1 2

⎡

⎣ ⎢

⎤

⎦ ⎥

€

A−1 =

2

11−

3

111

11

4

11

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

Solve the following system using Cramer’s Rule

€

x − 3y = 6

2x + y = 4

x = 18/7

y = -8/7

Find the roots of the quadratic

€

f (x) = 2x2 − 6x + 4

x = 1

x = 2

Solve.

€

f (x) =2

5x2 − x +

3

5

X = 1

X = 3/2

List the steps, in order, of solving

a quadratic via completing

the square method

1. Evaluate f(x) at 0.

2. Isolate the constant term.

3. If a does not = 1, divide by a.

4. Add the square of one half of the coefficient of x to both sides.

5. Factor one side to be the square of a binomial.

6. Square root both sides.

7. Solve for the variable.

Find a quadratic with the following roots:

x = 3 + 2i

x = 3 - 2i

€

f (x) = x2 − 6x +13

Find the first and second derivative of

€

f (x) = 5x9 −14x4 + 2x3 − 4x−3

€

′ f (x) = 45x8 − 56x3 + 6x2 +12x−4

€

′ ′ f (x) = 360x7 −168x2 +12x − 48x−5

Find a polynomial with the

given roots:

x = -2, 0, 1, 3

€

f (x) = x4 − 2x3 − 5x2 + 6x(or any scalar multiple)

Divide

(you may NOT use synthetic division)

€

3x4 − 2x3 + x − 8

x + 2

€

3x3 + 4x2 + 8x +17 +26

x + 2

Graph, labeling the critical points of the curve

(roots, extrema, inflection point).

€

f (x) = 3x3 + 6x2 + 3x