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U shape

y=x (squared)

vertex

the lowest and lowest point of the parabola

lowest point / minimum

if the parabola opens up then the vertex is where?

highest point / maximum

if the parabola opens down then the vertex is where?

what does (a) stand for

(a) determines if the parabola opens up or flips over the x-axis

if (a) is positive

the parabola goes up

if (a) is negative

the parabola goes down

the parabola is wide

if the fraction is <1

the parabola is narrow

if the fraction is >1

what does (b) stand for

whether the parabola shifts left or right

left

if (b) is positive it goes...

Right

if (b) is negative it goes...

what does (k) stand for

whether the parabola moves up or down

up

if (k) is positive then the parabola moves

down

if (k) is negative then the parabola moves

the y-intercept

what does (c) stand for

what does (bx) equal

helps with the axis is symmetry (-b/2a)

what does (ax squared) stand for

it does the same thing, it determines if it opens up or down

plug it in

the vertex is the point

-2ah

what does (b) equal

a>0

the parabola opens upward if

a<0

the parabola opens downward if

(-b/2a) , f(-b/2a)

the axis of symmetry is the vertical line x=

(c)

the y-intercept is

the domain is

all real numbers

the range is

all values > or equal to the minimum

(h,k)

vertex of a vertical parabola

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

standard form of a vertical parabola

x=h

Axis Of symmetry

[h,k+1/(4a)]

focus of a vertical parabola

y=k-1/(4a)

directrix of a vertical parabola

(h,k)

vertex of a horizontal parabola

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

standard form of a horizontal parabola

y=k

major axis

[h+1/(4a),k]

focus of a horizontal parabola

x=h-1/(4a)

directrix of a horizontal parabola

Standard Form of a Parabola

y=ax² + bx + c

Vertex Form of a Parabola

y=a(x − h)² + k

solutions

D=0, Dy=0; infinite solutions

n

Number of Solutions for a Polynomial of Degree n

The Quadratic Formula

x=[-b+/-√(b² − 4ac)]÷2a

The Vertical Motion Formula

h(t)=1/2at² + v₀ + h₀

a=-32 ft/s²

The Acceleration of Gravity (a)

Discriminant=D=(b² + 4ac)

How To Find The Number of Solutions Using the Discriminant

Parabola:

A set of points that are equidistant from a given point (focus) and a given line (directrix)

X-Oriented Parabolas:

*Open to the left or right

Y-Oriented Parabolas:

*Open up or down

X-oriented parabolas open to:

the left or right

X-oriented parabolas equation:

(y-k)^2 = 4p(x-h)

(h+p,k)

X-oriented parabolas focus:

x=h-p

horizontal parabola directrix

p>0

X-oriented parabolas open to the right if:

p<0

X-oriented parabolas open to the left if:

|p|

The distance from the vertex from the focus and the directrix

Y-oriented parabolas open:

Open up or down

Y-oriented parabola equation:

(x-h)^2= 4p (y-k)

(h,k+p)

parabolic focus

y=k-p

vertical parabola directrix

y= focus

(h, k+c)

y=k-c

y= directrix

vertex

The point where two sides meet. (Shared end points of the line segments of a polygon.)

x= focus

(h+c, k)

x= directrix

x= h-c