SOLUTION: Identify the vertex, axis of symmetry, and direction of opening for: y=1/2(x-8)^2+2. Thank you

Question 41896: Identify the vertex, axis of symmetry, and direction of opening for:
y=1/2(x-8)^2+2.
Thank you
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
First re-arrange the given equation to compare with standard form.

or

Let us transform the equation to the new co-ordinate system (X,Y) such that X=x-8 and Y=y-2.
Then the given equation becomes .
This is a parabola with the Y-axis as its axis.
Comparing with the standard equation , a=.

AXIS OF SYMMETRY AND DIRECTION OF OPENING
Here the axis of symmetry is x = 8 and as i.e. positive so the parabola opens upwards.

VERTEX
The vertex of the parabola is the point (X=0,Y=0) with respect to the new co-ordinate system.
Now, x=8+X and y=2+Y.
So when X=0 and Y=0, x=8 and y=2.
So the co-ordinates of the vertex w.r.t. the old co-ordinate system are (x=8,y=2)

FOCUS
The co-ordinates of focus of the parabola are (X=0,Y=a) in new co-ordinate system and so (x=8,y=2+a) in old co-ordinate system.
As here a=2 so the co-ordinates of the focus are (x=8,y=).

DIRECTRIX
The equation of directrix of the parabola is Y+a=0 in new co-ordinate system. Transferring to old co-ordinate system the equation is or .

RELATED QUESTIONS
Identify the vertex, axis of symmetry, and direction of opening for... (answered by stanbon)

Identify the vertex, axis of symmetry, and direction of opening for: y=1/2(x-8)^2+2. (answered by venugopalramana)

Identify the vertex , axis of symmetry, and direction of opening for y=2(x+3)^2-5.... (answered by Nate,venugopalramana)

how do you find the vertex, axis of symmetry, and direction of the opening of the... (answered by ewatrrr)

what is the vertex, axis of symmetry, and direction of opening for... (answered by lwsshak3)

Parabolas: Write each question in standard form. Identify the vertex, axis of symmetry... (answered by lwsshak3)

Identify the vertex, axis of symmetry , y-intercept, x-intercepts, and opening of each... (answered by josgarithmetic)

For each of the following quadratics, A. y=-2(x+1)^2+8 B. y=x^2+6x-16 -... (answered by drk)

I'm not sure if this is the right section. I have two question's with no textbook. 1.... (answered by jim_thompson5910)