Parabola's
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39 Terms
What is a parabola?
A Parabola is a set of points in a plane that are equidistant from a fixed line, the directrix, and a fixed point; the focus.
What is the focus?
A fixed point (dot) on a graph.
What is the directrix?
A fixed line on a graph.
What does equidistant mean?
Equal distance
Where is the vertex?
The vertex is in the middle of the directrix and focus point.
What is p?
The distance between the vertex and focus/ The distance between the vertex
What is the equation for a parabola?
y= 1/4p (x-h)2+k
The vertex point is represented by…
(h,k)
What is the equation for finding the focus?
(h,k+p)
What is the equation for finding the Directrix?
y=k-p (y is the directrix)
The parabola y= -(1/20) (x-3)2+6 has its focus as (3,1). Determine and state the equation of the directrix.
y=k-p. Find k and p
divide -20 into 4 (1/4p) and -5. p=-5 k=6
6-(-5)
directrix= 11
(4,7), 1, opens up.
(-7,0), 3, opens down.
Question is in picture
(-2,-2), 1, opens left
y=−(1/8)(x+4)2+1
y= -(1/12)(x+6)2-3
If the parabola opens down or left the p (thus the fraction) in the equation will become ____.
negative
y=-(1/4)(x+7)2-1
Question is in picture
y=-(1/4)(x+5)2-5
x=-(1/40) (y+1)2+1
when parabola’s are sideways the _,_ and the _,_ places are swapped.
when parabola’s are sideways the x,y and the h,k places are swapped.
If a up and down parabola’s are:
y= 1/4p (x-h)2+k
Than what are left and right parabola’s?
x=1/4p (y-k)2+h
y= -(1/16)(x+8)2-4
x=-(1/8) (y+1)2-3
x=1/4(y-7)2+5
How can you tell which direction the directrix is?
by checking the letter. For example x=0 is horizontal and y=0 is vertical. The symbol in the parenthesis tells which number from the vertex to use as well.
A parabola can be drawn give a focus of (-7,8) and a directrix of y=0. Write the equation of the parabola in any form.
y=1/16(x+7)2+4
A parabola can be drawn given a focus of (4,-7) and a directrix of y=-1. Write the equation of the parabola in any form.
y=-(1/12)(x-4)2-4
A parabola can be drawn given a focus of (4,-9) and a directrix of y=1. Write the equation of the parabola in any form.
y=-(1/20)(x-4)2-4
y=1/24 x2+4
What does h,k stand for in the parabola equation?
the coordinates of the vertex
What does p stand for in the parabola equation?
The distance between the focus and the vertex.
What is the equation for a parabola facing downwards?
y= -1/4p (x-h)2+k
What is the equation for a parabola facing upwards?
y = 1/4p (x-h)2+k
When a parabola is facing left or right you swap ____ and ____
x and y, h and k
When a directrix is x=___ what way will the parabola face?
Sideways because the resulting equation will be x=1/4p….. Look at the variable next to equal sign as the start of the equation.
When a directrix is y=___ what will the parabola face?
up or down because the resulting equation will be y=1/4p….. Look at the variable next to equal sign as the start of the equation.
What is the equation for a parabola facing left?
x= -1/4p (y-k)2+h
What is the equation for a parabola facing right?
x= 1/4p (y-k)2+h
