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Question 630464: X = - 1/4 y2 + y + 2
a. Put this equation in standard form for a parabola.
b. What direction does it open in?
c. What is the coordinate of the vertex?
d. Sketch the graph of the parabola.
e. Find one point on your graph, and test it on the original equation.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! X = - 1/4 y2 + y + 2
a. Put this equation in standard form for a parabola.
x=-1/4 y2+y+2
complete the square:
x=-1/4(y2-4y+4)+2+1
x=-1/4(y-2)^2+3
This is an equation of a parabola that opens leftwards.
Its standard form: y=-A(y-k)^2+h, (h,k)=(x,y) coordinates of the vertex
b. What direction does it open in? Left
c. What is the coordinate of the vertex? (3,2)
d. Sketch the graph of the parabola. Sorry, I don't have the means to graph it for you, but you should be able to graph it yourself using coordinates of the vertex and the y-intercepts found as follows:
set x=0
0=-1/4(y-2)^2+3
-1/4(y-2)^2=-3
(y-2)^2=12
y-2=±√12=±3.4641
y=2±3.4641
y=-1.4641
and
y=5.4641
e. Find one point on your graph, and test it on the original equation.
I will leave this one for you to do.
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