Algebra 2

one real solution

, we get two Real solutions. when it is zero we get just ONE real solution (both answers are the same) when it is negative we get two Complex solutions.

standard form

A general term meaning "written down in the way most commonly accepted" It depends on the subject: • For numbers it means "Expanded Form" (such as 125 = 100+20+5), but in Britain it means "Scientific Notation" • For equations it means the form: (some expression) = 0

axis of symmetry

A line through a shape so that each side is a mirror image

compression

A transformation in which a figure grows smaller. Compressions may be with respect to a point

parabola

For a given point, called the focus, and a given line not through the focus, called the directrix

reflection across x axis

It is basically a 'flip' of a shape over the line of reflection

no real solutions

The associated quadratic equation has exactly one real solution. The associated quadratic equation has one solution as x = 0. The associated quadratic equation has no real solution. The associated quadratic equation has one solution as x = 5.

GCF

The highest number that divides exactly into two or more numbers

vertex of a parabola

The vertex of a parabola is the point where the parabola crosses its axis of symmetry

how to find vertex when given standard form

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex.

vertex form

Vertex is the common point to join the two line segments. In parabola, vertex is the measurement of the maximum or minimum point in a curve. Vertex of the parabola is defined by using the quadratic equation.

discriminant

a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.

horizontal translation

a graph is equivalent to shifting the base graph left or right in the direction of the x-axis

zero of the function

also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x) = 0. In other words, a "zero" of a function is an input value that produces an output of zero (0).

quadratic function

equation as an equation of degree 2, meaning that the highest exponent of this function is 2.

stretch

he graph away from the x-axis

maximum value

highest point on graph

two real solutions

in other words the discriminant is a positive number), then the quadratic equation will have exactly two Real number Solutions. For example consider, x2 - 2x -8 whose discriminant would be (-2)2 - 4(1)(-8) = 36. Since 36 is greater than 0, there are two (unequal) Real solution

Factoring

is the process of finding the factors: Factoring: Finding what to multiply together to get an expression.

minimum value

lowest point on graph

equation for axis of symmetry

parabola and divides a parabola into two equal halves that are reflections of each other about the line of symmetry. It intersects a parabola at its vertex. It is a vertical line with the equation of x = -b/2a

vertical translation

s a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system

zero product property

simply states that if ab=0 , then either a=0 or b=0 (or both)

quadratic formula

x = -b ± √(b² - 4ac)/2a

y-intercept

y at the point where the line crosses the y axis.