2.1-2.4 Polynomial Functions

Quadratic Functions

100

Find the vertex of \[f(x)=9x^2-37\]

What is (0,-37)?

200

NO CALC Find the minimum value of the function \[f(x)=x^2-6x+2\]

What is -7?

300

Write the function in vertex form \[f(x)=x^2-8x+11\]

What is \[f(x)=(x-4)^2-5\]?

400

Write the function in vertex form \[f(x)=2x^2+8x+7\]

What is \[f(x)=2(x+2)^2-1\]?

500

Write the vertex form of the equation of a parabola that has a vertex (1,-2) and whose graph passes through (-1,14).

What is \[f(x)=4(x-1)^2-2\]?

Polynomial Functions of Higher Degree

100

Describe the end-behavior of the graph of the function f(x)=(x-4)^6

both sides up

200

Find all real zeros of the function \[g(x)=x^2-x-56\]

What is x = 8 and x = -7?

300

Find all real zeros of the function \[h(x)=6x^2-5x-4\].

What is -1/2 and x = 4/3?

400

Find all real zeros of the function \[m(x)=x^3+3x^2-4x-12\].

What is x = 2, -2, -3?

500

Write an equation in linear factorization form with degree 4 and given zeros: 3i, 2

f(x)=(x-3i)(x+3i)(x-2)²

Polynomial and Synthetic Division

100

Divide (x³-1)/(x-1)

x²+x+1

200

Divide (3x³+8x²+5x-7)/(x+2)

3x²+2x+1+ (-9/(x+2))

300

Divide [(2x^2+10x+12)\(x+3)].

What is 2x+4?

400

Divide (2x³-8x²+3x-9)/(x²+1).

2x-8 + [(x-1)/(x²+1)]

500

Use the remainder theorem and synthetic division to find f(2) for the function \[(2x^3-7x+3)\].

What is 5?

Complex Numbers

100

Find (12 + i) - (4 - 7i)

What is 8 + 8i?

200

i⁸

1

300

Write 6/(2-5i) in standard form.

(12/29) +(30/29)i

400

Find (9 + 2i)(2 - 4i)

What is 26-32i?

500

(i/(3-2i))+ (2i/(3+8i))

(62/949) + (297/949)i