34 terms

# Algebra II Formulas

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point slope form
y - y1 = m(x - x1)
slope intercept form
y= mx+b
difference of cubes
x³ - y³ = (x - y)(x² + xy + y²)
sum of cubes
x³ + y³ = (x + y)(x² - xy + y²)
x = -b ± √(b² - 4ac) / 2a
ax² + bx + c = 0
standard form for equation of a circle
(x - m)² + (y - n)² = r² if (m,n) was your center point
difference of squares
x² - y² = (x + y)(x - y)
imaginary numbers
√(-1) = i
sum of squares
x² + y² = (x² + xy + y²)
distance formula
d = √( x2- x1) + (y2 - y1)
midpoint formula
(x1 + x2 / 2 , y1 + y2 / 2)
a graph is symmetric with respect to the x-axis when (x,y)...
and (x, -y) is also on the graph
a graph is symmetric with respect to the y-axis when (x,y)...
and (-x,y) is also on the graph
a graph is symmetric with respect to the origin when (x,y)...
(-x, -y) is also on the graph
completing the square
x² + bx +( b / 2)² = (x + b / 2)²
principal square root of a number
√(-a) = √(ai)
slope of a line passing through two points
m = y2 - y1 / x2 - x1
a line is parallel if
slopes are equal EX: m1 = m2
line is perpendicular if
slopes are negative reciprocals EX: m1 = (-1 / m2)
a function is even if
f(-x) = f(x)
a function is odd if
f(-x) = -f(x)
greatest integer function is
vertical shift upward is
h(x) = f(x) + c
vertical shift downward is
h(x) = f(x) - c
horizontal shift to the right
h(x) = f(x - c)
horizontal shift to the left
h(x) = f(x +c)
reflection in the x-axis
h(x) = -f(x)
relection in the y-axis
h(x) = f(-x)
sum of a function
(f + g)(x) = f(x) +g(x)
difference of a function
(f - g) (x) = f(x) - g(x)
product of a function
(fg)(x) = f(x)g(x)
quotient of a function
(f / g)(x) = f(x) / f(x)
compostion of a function
(f o g)(x) = f(g(x))