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Level 526

Quadratic Functions


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Quadratic Function
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
Parabola
the graph of a quadratic function
Parent Function
the most basic function of a family of functions, or the original function before a transformation is applied
vertex
The point where two sides meet. (Shared end points of the line segments of a polygon.)
Axis of Symmetry
a line that divides a parabola in two equal halves and goes through the vertex
Minimum Value
The lowest point of a parabola (when a>0)
Maximum Value
The highest point of a parabola ( when a<0)
y=a(x-p)(x-q)
Intercept Form
quadratic equation
ax² + bx + c = 0
x-intercept
the point where the line crosses the x-axis
Square Root
when multiplying a number by itself to get a square number
Zero Of a Function
a value of x that makes the function's value zero
roots
ⁿ√r [ cos (Θ+2πk/n) + i sin (Θ+2πk/n)]
Perfect Square
the number that forms when two same numbers are multiplied together
Linear Function
y = mx + b
Exponential Function
y = ab^x
discriminant
b²-4ac
Perfect Square Trinomial
A trinomial, perfect square first term, perfect square last term, middle term is the square root of the last term doubled. It also factors into perfect square binomial.
Axis of symmetry (mathematically)
X = - b/2a
vertex has a x-coordinate of
X = - b/2a, (X,Y)
absolute value of a complex number
The absolute value of a + bi is the distance from the origin to the point (a,b) in the complex plane and is denoted |a+bi| = √a^2+b^2
binomial
A polynomial with two terms
completing the square
a process used to form a perfect-square trinomial
complex conjugate
the value of 1 represented by the denominator of a complex fraction with opposite sign
complex number
includes real and imaginary numbers
complex plane
coordinate system where real numbers intersect with imaginary numbers
imaginary number
the square root of a negative number
imaginary part
in complex number
imaginary unit
i, the square root of -1
quadratic inequality in two variables
an inequality that can be written in one of the following forms, y> or < ax^2 + bx + c, where a, b, and c are real numbers and
quadratic model
a quadratic function used to represent a set of data
quadratic regression
a statistical method used to fit a quadratic model to a given data set
real part
in complex number
root of an equation
any value of the variable that makes the equation true
standard form
ax^2 + bx + c = 0, where a, b, and c are real numbers and a cannot equal zero
trinomial
A polynomial with 3 terms
vertex form
y = a(x - h)^2 + k
vertex of a parabola
The midpoint between the focus and the directrix. (h,k)
Maximum
the highest possible y value for the graph of a quadratic function; also the y-coordinate of the vertex
Minimum
the lowest possible y value for the graph of a quadratic function; also the y -coordinate of the vertex
f(x)=ax²+bx+c
standard form quadratic
zeros
the x-intercepts of the graph of a function. The points for where y=0
Symmetry
A plane figure that can be folded along a line so the two parts match.
x intercept
value of x where y = 0
y intercept
y value where the graph crosses the y axis
vertex form quadratic
f(x) = a(x-h)² + k
expression
A mathematical phrase without an equal sign.
monomial
a number or a product of numbers and variables with exponents that are whole numbers
polynomial
A monomial or sum of monomials
y-intercept
the point where the line crosses the y-axis
minimum value of a function
The y-value of the lowest point on the graph of a function.
maximum value of a function
The y-value of the highest point on the graph of a function.
vertex form of a quadratic equation
A quadratic function written in the form f(x) = a(x - h)² + k, where a, h and k are constants and (h, k) is the vertex.
standard form of a quadratic equation
y = ax² + bx + c, where a is not equal to zero.
Quadratic Formula
x = -b±√b²−4ac / 2a
discriminant of a quadratic equation
The discriminant of the quadratic equation ax²+bx+c=0 is b²-4ac.
nonlinear system of equations
A system in which at least one of the equations is nonlinear.
difference of two perfect squares
A perfect square minus another perfect square. a² - b² = (a - b)(a + b).
Horizontal shift
# is inside ( ) that is being added or subtracted.
complete factorization over the integers
Factorization form that contains only prime factors.
Rate of change
A value that results from dividing the change in a function (y-values) of a variable by the change in the variable (x-values). It is another name for slope.
End Behavior
Look at HA
domain of a function
The set of all possible input values of a function.
range of a function
The set of all output values of a function.