Quadratic Equations
Complex Numbers
Systems of Nonlinear Equations
The Quadratic Formula
Random Math Facts
100
Write an equation of the parabola in standard form.
f(x) = -1/4 x^2 + x + 3
100
What are a pair of complex numbers that have the form
(a+bi) and (a-bi) called?
Conjugate Pairs
100
Solve the following system:
y=12x+20
y=10x+40
x=10, y=140
100
What is the Quadratic Formula?
x = {-b +- sqrt(b^2 - 4ac)}/{2a}
100
Can you comb a coconut without causing it to have a cowlick?
No, there will always be a cowlick according the "Hairy Ball Theorem"
200
What are the zeros (roots, or solutions) of the function:
f(x)=4x^2+3x-10
x = -2, 5/4
200
What is the expression
i^2
equivalent to?
-1
200
Solve the following system
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10
x=2, y=-1, z=1
200
What is the discriminant and what is it used for?
b^2-4ac
It is used to identify the number and types of solutions
200
On average, how many friends do you think your friends have? More, less, or the same?
On average your friends are more popular than you are.
300
Identify if the data below is quadratic or not, if it isn't what kind of data is it?
| Time (seconds), x | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 |
| Time (seconds), x | 3 | 31 | 51 | 63 | 67 | 63 |
Quadratic (Second difference test and position function)
300
Simplify the following expression:
(5+6i)+(-4-7i)
1-i
300
Solve the following system:
x-y=-1
y=-x^2+3
(-2,-1) and (1,2)
300
Using the quadratic solution identify the number and type of solutions to the following quadratic function (you may need to convert it to standard):
y = -3(x-4)^2+8
DO NOT SOLVE THE EQUATION
Two real solutions
300
On earth, is there any time that two points opposite each other on the surface will have the same temperature and humidity?
Yes, according to the Bursk-Ulam Theorem.
400
What is the graph of
y >= -x^2-4
400
Simplify the following expression:
(5-24i)+3i(5-3i)-(16-3i)
-2-6i
400
Solve the following system:
y=2x^2+3
y=-3x^2+4x+1
No solutions
400
Using any method (but the quadratic formula is encouraged) solve:
0 = x^2 - 3
+- sqrt(3)
400
What is the probability of finding a number that has no square divisor (other than one)?
6/pi^2
or about 61%
500
You and a friend decide to go into business selling bobblehead dolls. The profit p for selling b bobblehead dolls is given by the equation
p(b)=-0.2b^2+15b-150
. How many bobblehead dolls will you have to sell for your profit to be greater than $100?
25<b<50
or more than 25 but less than 50
500
Simplify the the following expression:
(1-i)(1+i)
2
500
What are the solutions to the system?
x^2+y^2=13
-3y=2x
(-3,2) and (3,-2)
500
Solve this quadratic equation:
y=2x^{2}-5x+7
\frac{5 +- i\sqrt{31}}{4}
500
Abraham Lincoln studied this famous mathematicians writings, and attributed this practice to his success in being a lawyer and politician. Which mathematician was it?
Euclid (The Father of Geometry)