What value of c will make this equation a perfect square?
[Form a(x-h)^2]
5x^2 - 10x + c
c = 5
100
Find the zeroes of the quadratic:
y = x^2 - 9
x = -3, x = 3
100
Multiply
|1| |2 5|
|5| |6 3|
Impossible
2x1 2x2
100
Find the solution to the following system of equations
3x + 6y = -9
9x = -3y + 12
(11/5, -13/5)
100
If I roll a standard die and get a 2, then flip the die over; what number is showing?
5
200
Complete the square to put this into vertex form
y = x^2 - 3 + 4x
y = x^2 + 4x - 3
(x+2)^2 = x^2 + 4x + 4
y = x^2 + 4x + 4 - 4 - 3
y = (x+2)^2 - 4 - 3
y = (x+2)^2 - 7
200
Given the function
y = 2 (x+2)^2 - 4
What is the location of the Vertex?
(-2,-4)
200
Multiply
|5 -2 7| |1 |
|0 1 2| |0 |
|0 0 3| |-2|
|-9|
|-4|
|-6|
200
Find the solution to the following system of equations
4x - 5y = 7
8x - 10y = 13
None, they never intersect
200
Who proposed the law of motion that for every action there is an equal and opposite reaction?
A. Albert Einstein
B. Isaac Newton
C. Galileo
B. Newton
300
Complete the square putting it into vertex form
2x^2 - 2y - 12x + 6 = 0
x^2 - y - 6x + 3 = 0
y = x^2 - 6x + 3
(x-3)^2 = x^2 - 6x + 9
y = x^2 - 6x + 9 - 9 + 3
y = (x-3)^2 - 6
300
A parabola passes through the following three points
(5,17), (-20,2), (19,17)
Find the equation of its Axis of Symmetry
x = 12
300
Convert the following into matrix form
3x + 4y = 7
3y = 6
|3 4| |x| = |7|
|0 3| |y| |6|
300
Find the solution to the following system of equations
8x = 2 + 4y
2y - 4x = -1
Infinite, all points along the line y = 2x - 1/2
300
What do you call the set of numbers that includes
-5,7,0,2,10
but not 1.5, pi, 7/3, or -9/2?
Integers
400
Complete the square, putting the equation into vertex form
y = 2x^2 + 8x
y = 2 ( x^2 + 4x)
(x+2)^2 = x^2 + 4x + 4
y = 2 (x^2 + 4x + 4 - 4)
y = 2 ( (x+2)^2 - 4)
y = 2 (x+2)^2 - 8
400
A parabola has a vertex at (5,1) and passes through the point (4,2)
What is the equation of the parabola in standard form?
y = a(x-5)^2+1
2 = a(-1)^2 +1
2 = a + 1
a = 1
y = (x-5)^2 + 1
y = x^2 - 10x + 26
400
Find the inverse of the following matrix
|15 -2 |
|-3 2/5|
Impossible
400
Two penguins are racing across a sheet of ice.
One penguin takes off running at .5 meter per second.
The second penguin takes deep breaths for 8 seconds, then leaps onto his belly sliding at 1.5 meters per second.
Express this as pair of equations, then solve:
How long until the second penguin passes the first?
y = .5*x
y = 1.5(x-8)
.5x = 1.5x - 12
x = 12
400
Dihydrogen Monoxide is a dangerous chemical used in nuclear power plants that kills thousands of people each year. By what name is it more commonly known.
Water
500
Complete the square, putting into vertex form.
y = -(1/2)x^2 - 6x + 2
y = -(1/2) (x^2 + 12x) +2
(x+6)^2 = x^2 + 12x + 36
y = -(1/2) (x^2 + 12x + 36 - 36) +2
y = -(1/2) ( (x+6)^2 - 36) +2
y = -(1/2)(x+6)^2 + 18 + 2
y = -(1/2)(x+6)^2 + 20
500
A parabola passes through the following three points
(1,48), (3,0), and (-11,0)
what is it's equation in standard form?
y = a(x-3)(x+11)
48 = a(-2)(12)
48 = -24a
a = -2
y = -2(x^2-3x+11x-33)
y = -2(x^2+8x-33)
y = -2x^2 - 16x + 66
500
Set up the following in matrix form, then solve
(you'll probably want to use your calculator)
2x+3y = 5
3x-2y+z = 0
x+2y-z = 3
??
500
A cannonball's height in meters with time follows this equation:
-10x^2 + 50x where x is seconds
A monkey with a jetpack's height starts at 0 and increases by 5 meters per second.
Assuming they launch at the same time; when will the monkey catch up to the cannonball?
-10x^2 + 50x = 5x
x = 0 is the starting condition, so remove it and divide by zero
-10x + 50 = 5
10x = 45
x = 4.5 seconds
500
What does the acronym LASER stand for?
Light Amplification by Stimulated Emission of Radiation