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Math
Algebra
Algebra 2 Vocab Words Semester 1
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Terms in this set (58)
opposite
the opposite of b is written -b. Two numbers that are the same distance from zero. Additive Inverse
reciprocal
the reciprocal of b is written 1/b. Multiplicative Inverse
power
a way to represent/write repeated multiplication
Ex:4^5 4=base (repeated factor) 5=exponent
base
repeated factor
Ex: 4^5 4 is the base
Variable
a letter used to represent unknown number(s)/value(s)
Terms of an Expression
part of an expression that is being added or subtracted
Ex: 3x+8y-7
Coefficient
a number being multiplied with a variable
Ex: 8y
Identity
a statement equating two (equivalent) expressions, an equation whose solution is all real numbers
equation
a statement that equates two expressions
equivalent equations
have same solution set
relation
any mapping/pairing of input and output values
domain
the set of all input values (x)
range
the set of all output values (y)
function
a relation in which every input had exactly one output
equation in two variables
a way to define or model a function
Ex: 3x+5y=7, y=-2x^2+8x-1
linear function
a function that can be written in the form y=mx+b, first degree fucntion. Slope can't equal 0. Graph is a line
function notation
a way to name a function
Ex: y=mx+b --> f(x)=mx+b
read as: "f of x"
means the value of f at x
parent function
for the family of all linear functions y=x
for the family of all absolute value functions y=l x l
for the family of all quadratic functions f(x)=x^2
y-intercept
the y-coordinate of a point where the graph intersects the y-axis, the point where the graph crosses the y-axis (0,y) substitute zero for x, solve for y
x-intercept
the point where the graph crosses the x-axis (x,0) substitute zero for y, solve for x
slope
the ratio of vertical change (the rise) to horizontal change (the run)
of a nonvertical line
Parallel Lines
if and only if the two lines have the same slope
perpendicular lines
if and only if their slopes are opposite reciprocal of each other
slope-intercept form
y=mx+b, the graph is a line with slope m and y-intercept b.
Standard Form of a Linear Equation
Ax+By=C, the graph is a line with intercepts x=C/A y=C/B m=-Ax/B b=C/B
point-slope form
y-y1=m(x-x1), the graph is a line with slope m and passes through the point (x,y)
direct variation
y=ax, a cannot = 0, the graph is a line that passes through the origin, a linear equation that can be modeled by the equation y=ax
constant of variation
a in the equation y=ax
linear regression
used to find a linear model that most closely follows the trend shown by a set of data points
scatter plot
a graph of a set of data pairs
correlation coefficient
a number denoted by r, from -1 to 1, that measures how well a line fits a set of data points
absolute value function
the distance the number is from 0 on a number line, abs value of x is lxl
extraneous solution
an apparent solution that must be rejected because it does not satisfy the original solution
Vertex of an Absolute Value Graph
the highest or lowest point on the graph of an absolute value function, the vertex of the graph y=l x l is (0,0)
transformation
changes a graph's size, shape, position, or orientation
translation
a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation
piecewise function
a system of equations-each with a specific domain (set of input values)
Solution of a System of Linear Equations in Two Variables
-point where graphs intersect
-ordered pair that makes both equations true
Linear Inequality in Two Variables
a system of two or more linear inequalities with an ordered pair that is a solution of each inequality in the system
linear programming
process of optimizing a linear objective function subject to a set of constraints
parabola
the U-shaped graph of a quadratic function
Vertex of a Parabola
the lowest or highest point on a parabola, the vertex for f(x)=x^2 is (0,0)
Maximum/Minimum value of Quadratic Function
for y=ax^2+bx+c, the vertex's y-coordinate is the minimum value of the function if a>0 and the maximum value if a<0
Intercept Form of Quadratic Equation
y=a(x-p)(x-q), also called factored form, the x-intercepts are p and q, the axis of symmetry is halfway between (p,0) and (q,0). It has the equation x=p+q/2, the graph opens up if a>0 and opens down if a<0
monomial
an expression that is a number, variable, or product of a number and variable(s)
binomial
the sum of two monomials
quadratic equation in one variable
written as ax^2+bx+c
radicand
the number s beneath the radical sign
rationalizing the denominator
the process of eliminating a radical from the denominator of a fraction
-rewrite the denominator as a rational number
conjugates
the expression a+*square root of b* and a-
square root of b
, used to rationaliz
square root of b
square root of b* and a-*square root of b*, used to rationalize the denominator, whose product is always a rational number
Imaginary Unit i
defined as i=
square root of -1
i^2=-1
imaginary number
a number not in the real number system represented as 'i', a+bi, b can't =0
Ex: 4+2i, -6-i, 1/4+2/3i
Pure Imaginary Number
0+bi, b can't =0
Ex: -6i, i, 1/3i
complex number
a number a+bi where a and b are real numbers. The number a is the real part of the complex number, and the number bi is the imaginary part
complex conjugates
two complex numbers of the form a+bi and a-bi
Quadratic Formula
Let a, b, and c be real numbers such that a can't =0. The solutions of the quadratic ax^2+bx+c are:
X=-b+/-
sq. root of b^2-4ac
/2a
b^2-4ac is the discriminant, can be used to solve ANY quadratic equation; when all else fails
Leading Coefficient
the coefficient of the term that has the highest degree of the equation and if put in correct form/order will be the coefficient of the first term
End behaviors
what graph is doing as x approaches +/- infinity, and f(x) approaches +/- infinity
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