MAT121 - Quadratic Equations (Ch. 9)

Complex Numbers

100

Subtract:

(-2-6i)-(4-7i)

-6+i

200

Multiply: 

6i(3+2i)

-12+18i

300

Simplify: 

i^43

i^3=-i

400

Multiply: 

(2+i)(5-3i)

13-i

500

Simplify: 

(6i)/(3-i)

-3/5+9/5i

Sq. Root Property & Completing the Square

100

2y^2=32

y=-4 or 4

200

(x-2)^2=9

x=-1 or 5

300

4(y+5)^2=4

y = -6 or -4

400

x^2+6x=7

x=-7 or 1

500

x^2+8x+25=0

x=-4-3i or -4+3i

The Quadratic Formula

100

x^2-2x-8=0

x=-2 or 4

200

y^2+11y+10=0

y=-10 or -1

300

x^2+2x-4=0

x=-1-sqrt5 or -1+sqrt5

400

7x^2+4x-5=0

x=(-2-sqrt39)/7 or (-2+sqrt39)/7

500

2y^2=3y+4

y=(3-sqrt41)/4 or (3+sqrt41)/4

Inequalities and Applications

100

Write the solution in interval notation:

x^2+2x-3<0

(-3,1)

200

Write the solution in interval notation:

x^2+2x-8>=0

(-oo,-4]uu[2,oo)

300

Write the solution in interval notation:

-x^2+x+2>=0

[-1,2]

400

The length of a rectangular poster is 1 ft more than the width. The diagonal of the poster is 5 ft. Find the length and width of the poster.

The length is 4 ft, the width is 3 ft

500

A height of a model rocket t seconds after being launched is given by 

h(t)=-16t^2+128t

How long is the rocket in the air?

The rocket is in the air for 8 seconds. (The height of the rocket is 0 feet for t = 0 and t = 8 seconds. This means the rocket is in the air 8 seconds before returning to the ground.)

Graphs of Quadratics

100

Identify the axis of symmetry:

f(x)=3x^2-12x+5

x=2

200

Identify the y-intercept:

f(x)=(x+2)^2-3

(0, 1)

300

Identify the vertex:

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

(1, -4)

400

Identify the vertex:

y=2x^2-4x+5

(1,3)

500

Identify the x- and y-intercepts:

f(x)=12x^2+5x-3

x-int:

(-3/4,0), (1/3,0)

y-int: 

(0,-3)