Quadratics Review
Complex Numbers
Factoring
Factoring Methods
Applications
100
How you can tell a function is a quadratic.
What is a degree of 2? (The highest exponent is 2)
x2
100
i = ____
What is
sqrt[-1] ?
100
Factor x2-11x+18.
What is (x-9)(x-2)?
100
The value for the new "C" term that would complete the perfect square
x2+12x+___=-5
What is 36?
100
The formula for the area of a rectangle.
A = l*w
200
The minimum or maximum point of a quadratic function.
What is the vertex?
200
i2 = ___
What is -1?
200
Solve using the square root method.
16x2-1=0
What is x = -1/4, 1/4?
200
The discriminant.
What is
b^2-4ac?
200
The part of the graph that represents the minimum or maximum value of the quadratic. For example, the tallest height of a thrown ball.
What is the vertex?
300
"x-intercepts," "roots," and "zeroes" all refer to ____________ of the function.
What are the solutions?
300
Find
sqrt[-324]
What is 18i?
300
Factor 2x2-32x+128.
Hint - look for the GCF.
What is 2(x-8)(x-8)?
300
The four possibilities for the discriminant and what they mean.
What is
d > 0 and is a perfect square, then there are two real, rational solutions
d > 0 and is not a perfect square, then there are two real, irrational solutions
d = 0, then there is 1 real, rational solution (they repeat)
d < 0, then there are no real solutions (2 complex/imaginary)
?
300
A quadratic graph models a ball being launched from the ground, soaring, then hitting the ground. The x-axis represents...
What is the ground?
400
Simplify (1+5i)(4-2i).
What is 14+18i?
Steps:
FOIL. 4 - 2i + 20i - 10i2
Combine like terms and simplify i2. 4 + 18i + -10(-1) = 14 + 18i
400
Factor and solve 8x2+10x=0.
What is x = -5/4, 0?
400
The quadratic formula.
What is
(-b+-sqrt[b^2-4ac])/(2a)?
400
The equation representing the area if you add x to the 8ft length and x to the 5 ft width.
What is A = (x+8)(x+5)?
500
Simplify
8/(12i).
What is
(-2i)/3?
500
Factor and solve
7x2-19x-6=0
What is x=-2/7, 3?
500
The area of a plot fenced in plot is 100ft2. The length = 20 and width = 5. Write an equation for if you doubled the area by adding x to the length and width.
What is (x+20)(x+5)=200?
600
Simplify
(3-6i)/(4-3i).
What is
(6-3i)/(5)?
600
Solve by completing the square
x2-8x-10=0
What is x =
4+-sqrt26?
600
The chicken coup at the petting farm is 10 feet by 14 feet. The farm would like to double the current area by adding the same amount, x, to the length and width. What are the dimensions of the new enclosure? Round to the nearest hundredth of a foot. Hint - you'll need the quadratic formula.
What is x = 4.85ft?