SOLUTION: The equation of a parabola is 12 y = ( x − 1 ) 2 − 48 12y=(x-1)2-48 . Identify the vertex, focus, and directrix of the parabola.
Algebra.Com
Question 1201701: The equation of a parabola is 12 y = ( x − 1 ) 2 − 48 12y=(x-1)2-48 . Identify the vertex, focus, and directrix of the parabola.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
********************
NOTE for future reference: the symbol "^" (shift-6) is commonly used to represent exponents. So you can write the equation for this problem as
12y=(x-1)^2-48
*******************
The x term is squared, so the graph opens up or down. The general vertex form of the equation of a parabola I prefer to use is this:
Note many references will show this equation in different equivalent forms; and different students have different preferences on which form to use. Some common equivalent forms are
[puts only "y" on the left]
[keeps the "4p" on the left so it is not a fraction]
In any of those forms, the vertex is (h,k); p is the directed distance (i.e., can be negative) from the directrix to the vertex and from the vertex to the focus.
Put the equation in your example in this form:
The vertex is (1,-4) and p is 3.
The directrix is p = 3 units below the vertex, at y = -7.
The focus is p = 3 units above the vertex, at (1,-1).
ANSWERS:
vertex (1,-4)
focus (1,-1)
directrix y = -7
RELATED QUESTIONS
Identify the vertex, focus, and directrix of the parabola.... (answered by stanbon)
1. Find the standard form of the equation of the parabola with a focus at (0, -9) and a... (answered by josgarithmetic)
Identify the vertex, focus, and Directrix of the graph of this parabola:
(x-1)^2 =... (answered by ewatrrr)
Identify the vertex, focus, and directrix of the parabola. x=-1/4(y+1)^2+2 Thanks (answered by lwsshak3)
Identify the vertex and directrix of the parabola (x+4)^2=-1/8(y+3)
and
Write the... (answered by lwsshak3)
identify the vertex, focus, and directrix of the problem.... (answered by stanbon)
For each equation of the parabola, (a) reduce to standard and then find the (b) direction (answered by josgarithmetic)
Identify vertex, focus, directrix, axis of symmetry and latus rectum from the following... (answered by Edwin McCravy)
what are the vertex, focus and directrix of the parabola: 12y=x^2-6x+45?
(x-3)^2=12(y-3)
(answered by lwsshak3)