Algebra Cram Flashcards
(18 cards)
Parallel vs. Perpendicular Lines
Parallel lines (||) have the same slope.
Perpendicular lines (⊥) have slopes that are negative reciprocals of each other.
What is vertex form?
What does and k represent?
y = a(x - h)^2 + k
Axis of symmetry = a, k = y value of vertex
a = open or closed circle
Two ways to get to the vertex form
Complete the square and move everything to one side.
Do -b/2a and then plug in to find the value of the vertex.
What is the discriminant and what does it represent?
b² - 4ac.
D > 0: The quadratic equation has two distinct real roots.
D = 0: The quadratic equation has one real root (a repeated root).
D < 0: The quadratic equation has two complex (imaginary) roots.
What does a negative skew indicate?
Symmetrical Distribution:
Evenly distributed on both sides
Mean ≈ Median ≈ Mode
Data is balanced around the center.
What is a residual?
Residual=ObservedValue−PredictedValue
Which is the correlation coefficient
r (not r squared)
What is a principal positive square root?
When you are evaulating any expression with a square root, (for example , the square root of four) the answer is always positive.
Difference of squares
a² - b² = (a - b)(a + b)
Sum of squares
NONE
Difference of cubes
a³ - b³ = (a - b)(a² + ab + b²)
Sum of cubes
a³ + b³ = (a + b)(a² - ab + b²)
What is set builder notation?
The domain is all real numbers greater than or equal to 3
{x∈R∣x≥3}
What is interval notation?
The domain is all real numbers greater than or equal to 3
[3,∞)
What should you do if you come across a simplify problem where the dmoinators are opposites
for example, x-2 in one fraction and 2-x in the other
Take out the negative from one of them, and then combine the fractions.
For example, 2-x becomes -(x-2). Then move the negative up!
What happens when you multiply a parabola? For example, x^2 becomes 4x^2
It gets narrower
What happens when you add to x inside the parenthesis?
F(x+1)
it moves 1 unit to the left
What does the discriminant determine?
b^2-4ac
if it equals zero, there is one real root
If it is a real number, there are 2 real roots
If it is a negative number, no real roots
