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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.