Quadratic Formula and Complex Numbers
Simplify.
(2 + 3i) - (8 + 6i)
-6 - 3i
y = (x+7)2 -11
(-7,-11)
What are the solutions to the following system of equations?
y = 3x2 - 4
y = -3x + 2
(-2,8) and (1,-1)
Simplify.
3i(7 + 2i)
-6 + 21i
What is the equation of the quadratic that has a vertex as (-3,7) and a=2?
y = 2(x+3)2 + 7
Teacher trivia question!!!!
Teacher has the answer on paper
Solve.
x2 + 4x + 20 = 0
x = -2 + 4i
x = -2 - 4i
What is the vertex of the equation?
y = x2 + 6x + 4
(-3,-5)
x2 - 6x -7 represents the time it takes a bouncy ball to land back on the ground. Which of the following solutions are NOT valid solutions?
x = -1
x = 7
Why?
x = -1 because time cannot be negative.
Simplify.
(7 - 9i)(3 + 2i)
39 - 13i
Where are the following located?
1) The vertex of a parabola
2) The focus of a parabola
3) The directrix of a parabola
1) ON the parabola
2) INSIDE of the parabola
3) OUTSIDE of the parabola
What are the values for x?
(x+5)(2x-3)=0
x = -5
x = 3/2
Solve.
2x2 + 4x = -10
x = -1 + 2i
x = -1 - 2i
DESMOS!!
Given the focus is at (3,4) and the directrix is at y=2, which of the following is the equation of the parabola?
a) (x-3)2=4(y-4)
b) (x-3)2=4(y-3)
c) (y-3)2=4(x-4)
d) (y-3)2=4(x-3)
B
What are the TWO WAYS to write the solutions of the following quadratic inequality?
x2-5x+6<0
a) (-2,-3) b) (2,3)
c) [-2,-3] d) [2,3]
e) -2<x<-3 f) 2<x<3
B and F
What are the seven transformations of functions?
Shift left (x+3)2
Shift right (x-4)2
Shift up x2+5
Shift down x2-6
Vertical stretch/horizontal compression 3x2
Vertical compression/horizontal stretch (1/2)x2
Reflect over the x-axis -x2