Essay Title: 

Unit 2 – Quadratic Functions

March 24, 2016 | Author: | Posted in mathematics, mathematics and economics

Unit 2 – Quadratic Functions

Part 1 Deliverable Length : 5 Pages

Instructions

Identify the document by typing your full name and section number next to the yellow text

Rename the by adding your last name to current name (e .g “u2ip_lastname .doc

Type your answers next to the yellow text

To show your work , you will need to include

the algebra used to compute the solution to any equations

the formula with substituted values

the final calculated answer with units

To utilize the scientific calculator on your computer , do [banner_entry_middle]

the following

Open the calculator (if it is not in the accessories folder , then select Run from the Start menu

Select View from the drop down menu

Select Scientific to utilize the calculator

Note that x^y computes any number to any power (integer , fraction decimal

1 ) Using the quadratic equation y x2 – 6x 8 0 , perform the following tasks

a ) Solve by factoring

FORMTEXT Answer : x1 2 , x2 4

FORMTEXT Show work in this space

y x2 – 6x 8 x2 – 2x – 4x (x2 – 2x ) – (4x – 8 x (x – 2 ) – 4 (x – 2 (x – 2 (x – 4

Hence : y (x – 2 (x – 4 0 . The equality can take place only if one of the multipliers is equal to zero . Thus : x1 2 , x2 4 are equation solutions

b ) Solve by using the quadratic formula

FORMTEXT Answer : x1 2 , x2 4

FORMTEXT Show work in this space

ax2 bx c 0

In our case : x2 – 6x 8 0

a 1 , b -6 , c 8

D (-6 )2 – 4 1 8 36 – 32 4

x1 (6 – ?4 /2 (6 – 2 /2 2

x2 (6 ?4 /2 (6 2 /2 4

Hence : x1 2 , x2 4

2 ) For the function y x2 – 6x 8 , perform the following tasks

a ) Put the function in the form y a (x – h )2 k

FORMTEXT Answer (x – 3 )2 – 1

FORMTEXT Show work in this space

y x2 – 6x 8 x2 – 2 3 x 9 – 9 8 (x2 – 2 3 x 9 ) – 9 8 (x2 – 2 3 x 9 ) – 1 (x – 3 )2 – 1

b ) What is the equation for the line of symmetry for the graph of this function

FORMTEXT Answer : x 3

c ) Graph the function using the equation in part a . Explain why it is not necessary to plot points to graph when using y a (x – h ) 2 k

FORMTEXT Show graph here

FORMTEXT Explanation of graphing

When function is in the form y a (x – h ) 2 k then it is clear , that in coordinate x , y (y y – k ) this function will take form of : y a (x – h ) 2 . It is also clear that if independent variables are x , y (x x – h y y – k ) function will be presented in from y ax ‘2 . It is not difficult plot the graph of function y ax ‘2 . That ‘s why to plot the graph of function y a (x – h ) 2 k it is enough… [banner_entry_footer]

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