Solving Quads by Square Roots
What must you have in front of your number EVERY TIME you finish taking the square root?
+-
Define i and what it's equal to.
i is defined as an imaginary number and is equal to
sqrt(-1)
Which coefficient/term do you work on in the quadratic when completing the square and what do you do with it to get your new c term?
You work with the b value and then you do (b/2)^2 .
What is the quadratic formula? You must get the entire equation correct to get the points.
x=(-b+-sqrt(b^2-4ac))/(2a)
What is the standard form of a quadratic when we are SOLVING or finding zeroes?
ax^2+bx+c=0
Solve 3x^2=48
+-4
Solve for x and y to satisfy the equation.
-1+10i=-x+3yi
x=1
y=10/3
Find the new c in x^2+6x+c
c=9
Find the values of x using the Quadratic Formula in x^2+3x-4=0
x=-4 and x=1
How many REAL solutions do you have if the discriminant is ZERO?
ONE
Solve (k-3)^2=121
k=14 and k=-8
Write your answer in STANDARD FORM.
14-(17-7i)+8i
-3+15i
Complete the square and solve for x in x^2+4x-12=0 .
x=2 and x=-6
Find the discriminant and describe the type of solutions of the equation.
5x^2-4x+2=0
Discriminant: -24
Type of Solutions: two imaginary solutions
With the given starting part of the quadratic formula:
(3+-sqrt((-3)^2-4(1)(-9)))/2, what is the quadratic equation?
x^2-3x-9
Solve (2z-5)^2=81
x=7 and x=-2
Following the pattern of i=sqrt(-1), i^2=-1, i^3=-i, and i^4=1, what is i^317?
i
Complete the square and solve for s in s^2+14s-9=0
s=-7+-sqrt(58)
Solve using the Quadratic Formula
-4x^2+6x-2=0
x=1 and x=1/2
Why is i^4=1 ?
Because i^2*i^2=i^4 and (-1)*(-1)=1
Solve 25(x-1)^2=49
x=-2/5
x=12/5
Write your answer in STANDARD FORM.
(6-4i)^2
20-48i
Write the quadratic function in vertex form. Then identify the vertex.
h(x)=x^2+22x+96
Equation: h(x)=(x+11)^2-25
Vertex: (-11,-25)
Solve using the quadratic formula
x^2+4x+5=0
x=-2+-i
Explain each step that happened below when solving (6-2i)(8-3i). You MUST get it all down correctly to get the points.
48-18i-16i+6i^2
48-34i+6i^2
48-34i+6(-1)
42-34i
1) FOIL or Distributive Property
2) Combine Like Terms
3) Definition of i^2=-1
4) Combine Like Terms, Simplify, or Subtraction