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Level 501

Parabolas


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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