Solving Systems of Equations
What are the two methods we use to solve systems of equations?
What is substitution and elimination?
From the general form:
f(x) = a(x-h)^2+k
How do the h and k values transform the graph?
What is the formula for the Discriminant?
b^2-4ac
What is the first step here if I want to solve using the Square Root Property?
x^2-8x+16=10
Factor the perfect square trinomial on the left side of my equation!
When solving quadratic systems we normally end up with 2 instead of 1 what?
Solutions!
What is my favorite kind of music?
Jazz
Solve
2 x − y = 9
x + 3 y = − 6
(3, -3)
From the general form:
f(x) = a(x-h)^2+k
What 3 transformations can the (a) value do?
If a is negative it reflects, if it's greater than 1 is stretches, and if its in between 0 and 1 it compresses.
What is the quadratic formula?
(-b+-sqrt(b^2-4ac))/(2a)
What is the first step here if I want to solve by Completing the Square?
x^2-8x-65=0
Add the 65 to the right side.
Solve:
y=x^2-5
y=x-3
(2,-1) and (-1, -4)
If i wasn't teaching what would I be doing for a living?
2 Options:
1. Ceramic Artist/Professor
Solve
x-3y=-12
2x+y=11
(3,5)
Describe the Transformations:
f(x) = -3(x-2)^2
Reflected, stretched, shifted right 2 units
Solve using the quadratic formula:
x^2+3x+2
x = -1, -2
What is the new C value in this step of completing the square?
x^2-8x=65
Solve:
y=-2x+2
y^2=2x
(2, -2) and (1/2, 1)
What state was I born in?
Alaska
Solve
2x+y+z=7
2x-y+2z=6
x-2y+z=0
(1,2,3)
Describe the Transformations:
f(x) = 1/2x^2-2
Solve using the quadratic formula:
6x^2-7x-3
x = 3/2, -1/3
Solve by using the square root property
x^2+16x+64 = 4
x= -10, -6
Solve:
y-x^2=7x+12
y=x+7
(-5, 2) and (-1, 6)
How long have I been married?
6 months (since July)
Solve
-4x-5y-z=18
-2x-5y-2z=12
-2x+5y+2z=4
(-4,0,-2)
Describe the transformations:
f(x) = -1/6(x+4)^2+2
Reflected, Compressed, Shifted left 4 units, Shifted up 2 units
What is the discriminant and describe the number and type of solutions you would get:
x^2+3x-10
Discriminant: 49
2 real rational solutions
Solve by Completing The Square
x^2-8x-65=0
x = 13,-5
Solve:
x-y+1=0
y^2-4x=0
(1,2)
What famous magazine have I been in?
Hint: Fashion
Vogue