Factor Completely
9x2 - 6x + 1
(3x-1)(3x-1)
Solve:
2x2 - 9x = 18
{-3/2, 6}
Write the equation of a line that passes through (-1, -2) and (-2, 4)
y - 4 = -6(x + 2) or y + 2 = -6(x + 1)
Solve:
6|1 - 5x| - 9 = 57
{-2, 12/5}
Perpendicular Slope (Negative Reciprocal)
3x4 - 12x3 - x + 4
(3x3-1)(x-4)
Solve:
(x-3)2 + 5 = 9
{1, 5}
Write the equation of a line that passes through (-5, 6) and is normal to 4x - 3y = 1
y - 6 = -3/4 (x + 5)
Solve the inequality:
| 2x + 1 | <= 3
[ -2, 1]
Which type of equations do you have to check on this Unit Test?
Absolute Value Equations
x4 - 13x2 - 48
(x+4)(x-4)(x2 + 3)
Solve:
x4 - 29x2 +100 = 0
{-5, -2, 2, 5}
Solve:
2x2 + 2x <= x2 + 8
[-4, 2]
Find the inverse of the function:
f(x) = (3x + 5) / 2
f-1(x) = (2x - 5) / 3
Find the average rate of change for g(x) = -2x2+ 3x - 1 over the interval [-1, 2]
slope = 1
3y4 - 24y
3y(y - 2)(y2 + 2y + 4)
Solve by completing the square:
x2 - 8x +18 = 0
4 +/- i sqrt(2)
Solve:
x3 + 3x2 - 10x > 0
(-5, 0) U (2, inf)
Solve the inequality:
| 1 - 4x | > 5
( -inf, -1 ) U ( 3/2, inf )
What is the standard form of a quadratic equation?
ax2 + bx + c = 0
3x4 - 27y6
3(x2 - 3y3)(x2 + 3y3)
Solve by completing the square:
2x2 - 4x - 7 = 0
1 +/- 3/sqrt(2)
Solve:
12x2 + 10x >= 12
(-inf, -3/2] U [2/3, inf)
Find the inverse of the function:
f(x) = (3x + 1) / (5 - x)
f-1(x) = (5x - 1) / (x + 3)
What must be true about f(x) in order for its inverse to be a function?
f(x) must be a one-to-one function OR
f(x) must pass the VLT & HLT