Step 2 - 172 - Conics Lab Assignment.sagews

Intro to working in Sage

Tips:

1. To execute a command, hit "Run" or press "shift+enter".

2. Multiplciation must be written as , e.g. 4x must be typed 4x

3. To define variables use =, in an equation use == to represent the equals sign.

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Practice:

- Part 1: Practice evaluating expressions and basic equations

1. Evaluate 1/2+3/7, show answer as a fraction and decimal

2. Simplify the expressions: 5*(x-3)+(x-3)^2+7x

3. Assign the value of -5 to a and evaluate a^2-3a

4. Define y as a variable

5. Solve 5y^2-8y-4=0

6. Solve the system 5x+3y=13, -3x-2y=-9

- Part 2: Practice Graphing functions and equations

5. Define f(x)=-3x+6 (explicit)

6. Plot f(x) on the window [-3,3]x[-3,15]

7. Graph the equation 3x+2y=12 (implicit)

ASSIGNMENT - Part 3: Conics and systems practice

1. Graph the conic equation 3x^2+6x+2y^2-8y-5=0, on an appropriate window

2. Graph the equation x+2=-4(y-1)^2 on an appropriate window

3. Solve the system of equations x^2-2xy+y^2=7, x^2-2xy+y^2=1

Part 1 - you will see examples worked out for each problem. Copy the code and change it for the assigned problem!

#1. Evaluate 1/2+3/7, show answer as a fraction and decimal
#example:
2/3+4/9
(2/3+4/9).n()

1.11111111111111

1/2+3/7

13/14

#2. Simplify the expressions: 5(6x-3)+(x-3)^2+7x
#example:
4*(2*x+4)-2*(x+4)-10*x

-4*x + 8

5*(6*x-3)+(x-3)*(x-3)+7*x

(x - 3)^2 + 37*x - 15

#3. Assign the value of -5 to a and evaluate a^2-3a
#example:
b=4
b^3-2*b

56

#4. Define y as a variable
#example: 
z=var('z')
z

z

#5.  Solve 5y^2-8y-4=0
#example:
solve(z^2-5*z-6==0,z)

[z == 6, z == -1]

#6. Solve the system 5x+3y=13, -3x-2y=-9
#example:
var('y')
solve([2*x-y==-4,-5*x+2*y==2],(x,y))

y [[x == 6, y == 16]]

Part 2: Graphing functions and equations

 #5. Define f(x)=-3x+6 and evaluate f(3),f(-1),f(0) and f(b)
#example
g(x)=2*x-4
g

x |--> 2*x - 4

var('b')
(g(3),g(-1),g(0),g(b))

b (2, -6, -4, 2*b - 4)

#6. Plot f(x) on the window [-3,3]x[-3,15]
#example:

plot(g(x),(-3,3))

#7. Graph the equation 3x+2y=12 (implicit)
#example:  
var('x y')
implicit_plot(2*x-y==4,(x,-3,3),(y,-5,5),axes=true,aspect_ratio=.6)

(x, y)

#OR you can define f(x,y)=2*x-y-4, and plot f(x,y)
f(x,y)=2*x-y-4
implicit_plot(f,(-3,3),(-5,5))

Part 3 Your turn to apply the above to conic sections!

1. Graph the conic equation 3x^2+6x+2y^2-8y-5=0, on an appropriate window

2. Graph the equation x+2=-4(y-1)^2 on an appropriate window

3. Solve the system of equations x^2-2xy+y^2=7, x^2-2xy+y^2=1