Quadratic expressions



Quadratic Expressions

Part 1

Show all of your work in a Word document and submit by the end of the module.

1-4: Solve by factoring:

4x2 - 25 = 0

(2x-5)(2x+5)=0

x2 - 12x + 36 = 0

(x-6)(x-6)=0

x2 + 14x + 45 = 0

(x+5)(x+9)=0

6x2 - x - 15 = 0

21-x=0

5-7: Solve by completing the square.

x2 - 4x + 3 = 0

x2 - 4x = -3

(x-2) 2 = -3+4

(x-2) 2 = 1

X=1 or 3

x2 + 5x - 1 = 0

x2 + 5x = 1

(x+) 2 = 1+

(x+) 2 =

x=

2x2 + 7x - 15 = 0

x2 + x =

(x+) 2 = +

x=

8-10: Solve by using the quadratic formula:

x2 + 9 = 0

Here,

a= 1, b= 0, c= 9

Using formula,

x2 - 3x + 4 = 0

Here,

a= 1, b= -3, c= 4

Using formula,

2x2 + 3x = 6

Here,

a= 2, b= 3, c= -6

Using formula,

Given the quadratic expression x2 + 4x + c, determine the value of “c” such that the equation has 2 real solutions. Repeat and find “c” such that the equation has 1 real solution. Finally, repeat such that the equation has no real solutions.

Assignment Expectations:

Recognize quadratic equations

Solve quadratics equations by factoring, completing the square and by applying the quadratic formula

Interpret the determinant for quadratic equations

Part 2

This SLP provides some insight into the use of quadratic formulas in business and natural science.

A company's costs, in millions of dollars, are given by the equation, C = x2 - 3x - 27, where x is the number of items sold, in thousands.  What are the costs when 1,000 items are sold? 1,500 items?

Answer:

C(x) = x^2-3x-27

C(1000) = 1000-3000-27 = 996973

C(1.5) = 1500 - 3*1500 - 27 = 2.25 - 4.5 - 27 = 2245473

A company's costs, in millions of dollars, are given by the equation, C = x2 - 3x - 27, ...