Presidential Debate

In my opinion the debate was every where. Romney seemed like he didnt know what he was talking about at all. I mean, what does he know? How are you going to have a degree from Harvard and not know what the laws are. Obama had to correct him about 4 or 5 times. It seemed as if Obama was straight on and got to the point, but Romney seemed nervous and like he thought of what to say about ten mintutes before the debate started. Thats all i have to say about this today ...
#TeamObama

NOTES

y=a(x-p)(x-g)
X Intersepts

• Solve for a
• Write a equation
• Leave in form y=a(x-p)(x-g)

y=ax^2+bx+c

• 3 pts/ 3 equations
• Solve the system for a,b,c
• Plug into equation y=ax^2+bx+c

y=a(x-h)^2+k
Vertex: (h,k)
Point: (x,y)

• Solve for a
• Use a,h,k
• to write an equation y=a(x-h)^2+k

Graphs !!!

Standard form of a quadratic equation.

y  =  x² + bx + c

Standard form of a parabolic equation.



y  =  a(x - h)²  + k

vertex (h, k)

• If you change a it makes the graph open up or down
  • Up when a is positive.
  • Down when a is negative.
  • Fractions (0 < a < 1) make the parabola wider.
  • Numbers (a > 1) make the graph narrower.

• Changing h, h is the number inside the ( ) that moves the parabola to the right or left.
  • you have to move it in the opposite direction.

 

• if you have (x + 2)² the graph moves two places to the left.
• if you have (x - 3)² the graph moves three places to the right.

• Changing k, k is the number outside the ( ) that moves the parabola up or down.

 

• if you have (x)² + 2 the graph moves up two places.
• if you have (x)² - 3 the graph moves down three places.

Z-Score

• Difference of two squares
  • a²- b² = (a + b)(a - b)
    •  x²-25= (x+5) (x-5)
    • x²-
• Trinomial perfect squares
  • a² + 2ab + b² = (a + b)(a + b) or (a + b)²
    • 3 examples
  • ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
    • 3 examples
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Binomial expansion
  • (a + b)³ = Use the pattern
  • (a + b)⁴ = Use the pattern

Zero Discriminant

• Zero Discriminant
• 1 real solution

Positive Discriminant

• Positive Discriminant, crosses the X- axis
• 2 real solutions

Negitive Discriminant

•  Positive Discriminant
• 2 real solutions

Quadrilaterals

Quadrilaterals

• four sides
• sum of the interior angles is 360 degrees

Kite

• 2 pair of congruent sides
• consective sides are not congruent

Parallelogram

• both pairs of oppisite sides are congruent
• both pairs of oppisite angles are congruent

Rectangles

• 4 right angles
• diagonals are congruent

Rhombus

• parellelogram with 4 congruent sides
• diagonals are perpendicular
• pair of oppisite angles

Square

• all sides are congruent
• angles are are congruent
•  diagonals intersect at 90 degrees

Trapizoid

• 1 pair of parellel sides