which is
which has
which is where
which has
where
where
with
if there is
which is
if they have
which is
to show
to show
which uses a
and then
or
which may have
that are
to calculate
to find potential
by
by using
to create
by
it is a
it is a
where if
where if
which is
which informs about the
which is used by
which find
to find
to find
which is
such as
where
which is
where
which is
where
which can be
which can be
that represents
that represents
by using
by
by using
which has
which has
with isolating
with isolating
such as
by
with the formula
which means
thus
therefore
therefore
therefore
where if
where if
where if
which can show the
to show
which is shown as
which involves the
which is
by using
by using the
by exploring
such as the
such as the
that involves
which involves
use
which is
use
if
if
if
to go from
if
which is solved by
which is
by
by using
by using
which means
with
that is displayed in
with a
involves
is used for
relates to the
involves
are shown in
to find
which informs about the

QUADRATICS

Quadratic Equations

Simplied Form

y=x^2

3 Models

Factored Form

y= a(x-s)(x-t)

Standard Form

y=ax^2+bx+c

Vertex Form

y=a(x-h)^2+k

Solving Quadratic Equations

Finding X Intercepts

Quadratic Formula

x = -b ± √b^2 - 4ac
________________
2a

BE

Discriminant is negative, there will be no roots. If 0, 1 root.

Factoring

Standard Form to Factored Form

Perfect Square Trinomial

Difference of Squares

a2 – b2 = (a + b)(a – b)

a=1

Use Simple Trinomial Factoring

lal>1

Use Complex Trinominal Factoring

Completing the Square

Standard Form to Vertex Form

Isolating X for roots

Solving of Parabola Characteristics

Roots/Zeros

Quadratic Formula

x=b2-4ac/2a

Discriminant

b^2-4ac

Nature of Roots

b^2-4ac > 0

There are 2 Real Roots

b^2-4ac = 0

There is 1 Real Root (Vertex is on x-intercept)

b^2-4ac < 0

There are no Real Roots

Showing Imaginary Relations(i)

Perfect Square

The Discriminant is a perfect square, thus making it a rational number that does not need the Quadratic Formula.

Factored Form

a(x-s)(x-t)=0

setting each factor to zero to solve

2(x-4)(x+5)=0

x-4=0 x=4

x+5=0 x=-5

Vertex

A (x) value

The Axis of Symmetry (h)

A (y) value

The Optimal Value (k)

A Maximum Value

The parabola opens down and is the highest point on the parabola.

A vertical line that divides the parabola into two congruent halves

A Minimum Value

The parabola opens up and is the lowest point on the parabola.

Vertex Form

y = a(x-h)^2+k

(h,k) represent V(x,y)

y = 2(x-4)^2+7 V(4,7)

Completing the Square

Converting Standard Form to Vertex Form

The (h,k) values

Factored Form

The Roots (x1,x2)

The (h) value with x1+x2/2=h

Subsitituing h into the previous parbola equation to find the y/k of the vertex.

The (a) value

Vertical Stretch/Compression

A magnitute change to the base parabola

0<a<1

A Vertical Compression

a>1

A Vertical Stretch

Graphing Parabolas

Plotting Points

A Symmetrical Open Plane Curve

Equations

Roots/Zeros

Coordiniates of the Parabola meeting the x-axis

0,1 or 2 Roots

Y-Intercept

Using 5 Existing Points to find Y-Intercept

PLOTTING THE VERTEX AND USING STEP PATTERN

Adding 5 more points onto the parabola from your equation

Differential Values

Table of Values

Second Differences

The relationship between the First Difference Values

A constant relationship states a quadratic relation

EXAMPLE

First Differences

The relationship between the consecutive y-values

A constant relationship states a linear relation

EXAMPLE

Direction of Opening

The (a) value

If a>0, the Parabola opens up.

If a<0, the Parabola opens down

Vertex

A (x) coordinate

Axis of Symmetry

Parabola meets Axis of Symmetry to split into two equivalent halves

A (y) COORDINATE

Optimal Value

The Highest(Maximum or Lowest(Minimum) point on the parabola