Unit 5 Review: Polynomials

Quadratic Graphs

100

What is the name of the line that divides the a quadratic function graph exactly in half?

Axis of symmetry

200

What is the y-intercept of the quadratic equation?

f(x)=4x^2-16x+15

(0,15)

300

What are the x-intercepts of the quadratic equation?

f(x)=4x^2-16x+15

(3/2,0) and (5/2,0)

400

What is the vertex of the quadratic equation?

f(x)=4x^2-16x+15

(2,-1)

500

Graph the polynomial function accurately. Identify the x-intercepts, y-intercept, and vertex.

f(x)=-2x^2+4x+6

x-intercepts:  (-1,0) and (3,0) 

y-intercept:  (0,6) 

vertex:  (1,8) 

Quadratic Equations

100

Find the zeros (solutions) of the following:

x(x-5)=0

x=0 and x=5

200

Find the zeros (solutions) of the following equation:

x^2 -8x -20

x=10 and x=-2

300

Solve the quadratic equation by factoring:

x^3+2x^2-15x

x={-5,0,3}

400

Solve the quadratic equation using the quadratic formula:

9k^2=4+7k

k=(7+-sqrt(193))/18

500

Solve the quadratic equation by completing the square:

2n^2=-12n-10

n={-1,-5}

Polynomials

100

Expand the polynomial expression:

(4x-3)^2

16x^2-24x+9

200

Give an example of these four types of polynomials:

1. Constant Monomial

2. Quadratic Trinomial

3. Linear Binomial

4. Cubic Monomial

Answers vary

300

Multiply the polynomials:

(2x-5)(4x+7)

8x^2-6x-35

400

Simplify the polynomial expression. Write your answer in standard form.

(3x^2-4x^3+2x)+3(x+1)-4(x^2-3+6x)

-4x^3-x^2-19x+15

500

Multiply the polynomials. Write your answer in standard form.

(x-2)(2x+1)(x-5)

2x^3-13x^2+13x+10

Factoring

100

Factor the polynomial:

x^2-64

(x-8)(x+8)

200

Factor the polynomial:

4x^2-20x+25

(2x-5)^2

300

Factor the polynomial: 

3x^2+15x+12

3(x+4)(x+1)

400

Factor the polynomial:

6x^2+19x+10

(3x+2)(2x+5)

500

Factor the polynomial:

yz^2-y^3+z^3-y^2z

(z-y)(z+y)^2

Miscellaneous

100

What is the quadratic formula?

x= (-b+-sqrt(b^2-4ac))/(2a)

200

What room number are you in right now?

Answers vary

300

What is the mistake? What should the answer be?

x^2+2x-4x^2+3x=-3x^2+5x^2

Do not add exponents when combining like terms. The answer should be  -3x^2+5x 

400

Write the three forms of a quadratic equation and what feature of a quadratic graph they are each useful for finding.

Standard Form (y-intercept)  y=ax^2+bx+c 

Intercept Form (x-intercepts)  y=(x-p)(x-q) 

Vertex Form (vertex)  y=a(x-h)^2+k 

500

A triangle has an area of 6 in², a base of (2x) inches, and a height of (2x+1) inches. Find the value of the base and height.

Base is 3 inches, height is 4 inches