Math 2 Module Review
completing the square
(change standard to vertex) divide b by 2 and square it, insert it after b and as a negative after c
Factor Form
(x-r1)(x-r2) r1 and r2 are x-int
Quadratic Translation
+ up, - down, (+) left, (-) right
zero exponent
0
Solving a quadratic inequality
1) Rewrite the inequality so that 0 appears on the right side. 2) Factor, or complete the square. 3) Pick test numbers 4) test the chosen numbers
perpendicular bisector
A line that is perpendicular to a segment at its midpoint.
Reflection
A transformation that "flips" a figure over a mirror or reflection line.
Dilation
A transformation that changes the size of an object, but not the shape.
4 term factoring
Grouping, look for GCF (inside) (outside)
Side Splitter Theorem
If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
triangle median
In a triangle, it is the line segment drawn from a vertex to the midpoint of its opposite side.
Quadratic Dilation
Multiplication: >1 stretch, 0<1 compress
2 Term Factoring
Perfect Square: (good twin) (bad twin)
SOH CAH TOA meaning
SOH (sin0=opposite/hypotenuse) CAH (cos0=adjacent/hypotenuse) TOA (tan0=opposite/adjacent)
Similarity Theorem
SSS or SAS or AA
Five ways to prove triangles are congruent
SSS, SAS, ASA, AAS, HL
Direct Variation
Y = kx, K = y/x
combined variation
Y=(kx)/z, K=yz/x
Complex numbers
a + bi (real + imaginary)
radical function
a function that contains the root of a variable
altitude
a line segment drawn from the vertex, perpendicular to the opposite side
transversal line
a line that intersects two or more lines, creating congruent and supplementary angles
angle bisector
a ray that divides an angle into two congruent angles
index number as the root of a to a power
a to the power of the power divided by the index
Vertex Form
a(x-h)^2+k
3 term factoring
ac X b (divide factors by a if a doesn't = 1)
Triangle angle sum theorem
all angles add up to 180
Standard Form
ax^2+bx+c
Rotation
circular movement around an axis such as the shoulder joint
Negative in exponents
flip to the other side of the fraction and turn positive
Translation
movement across a graph
x^2 times x^3
multiplication = addition x^(3+2)
double exponents
multiply (x^2)^3 = x^2 times 3
Quadratic Reflection
negatives: x axis, (y axis)
Imaginary #s
square root of -1 = i
angle of elevation/depression
the angle formed by a horizontal line and the line of sight to an object above (below) the horizontal line.
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
rational function
y=1/x
Inverse Variation
y=k/x, k=xy
joint variation
y=kxz, k=y/xz
