Show:
Graphing
Factoring
Imaginary Numbers
Completing the Square/Quadratic Formula
Misc.
100
What is the formula for the x-coordinate of the vertex?
x = -b/(2a)
100
Solve by factoring: x^2 - x - 20 = 0
x = -4 and 5
100
Simplify: (10i)(-4i)
40
100
Solve using the Quadratic Formula: x^2 - 3x - 4 = 0
x = -1 and 4
100
What is the formula for the determinant?
(b^2) - 4ac
200
What is the equation of the axis of symmetry for f(x) = 3x^2 - 4x + 12?
x = (2/3)
200
Solve by factoring: 4x^2 + 24x = 0
x = -6 and 0
200
Simplify: (7-i)(9+i)
64-2i
200
Solve using the Quadratic Formula: 9x^2 + 12x + 4 =0
x = (-2/3)
200
What is the formula for the Quadratic Formula?
x = (-b + or - the square root of (b^2)-4ac) / (2a)
300
What is the y-intercept of f(x) = -6x^2 + 4x - 7?
(0,-7)
300
Solve by factoring: 2x^2 - 5x - 12 = 0
x = 4 and (-3/2)
300
Simplify: (6+4i) - (10-2i)
-4+6i
300
Solve by Completing the Square: x^2 - 2x - 1 = 0
x = 1 plus or minus the square root of 2
300
How do you find the "c" when Completing the Square?
c = (b/2)^2
400
What is the vertex of f(x) = 2x^2 - 12x + 3?
(3,-15)
400
Completely Factor: 4x^4 - 64 = 0
4(x-2)(x+2)(x^2+4)
400
Simplify: (4+5i) / (3-2i)
(2/13) + (23/13)i
400
Solve by Completing the Square: x^2 - 8x + 24 =0
x = 4 plus or minus 2i the square root of 2
400
Write a quadratic equation with -2 and (1/3) as its roots. Write the equation in the form ax^2 + bx + c = 0, where a, b, and c are integers.
3x^2 + 5x - 2
500
What is the minimum value of f(x) = x^2 + 6x - 11?
-20
500
Completely Factor: 3x^4 - 18x^3 + 4x - 24 = 0
(3x^3+4)(x-6)
500
Simplify: (square root of -45)(square root of -14)
-3 square root of 70
500
Solve by Completing the Square: 5x^2 - 6x = 8
x = 2 and (-4/5)
500
Explain what types of solutions occur when the determinant is: a) > 0 and a perfect square b) > 0 and not a perfect square c) = 0 d) < 0
a) 2 real, rational solutions b) 2 real, irrational solutions c) 1 real, rational solution d) 2 complex (imaginary) solutions