- #1
Jshua Monkoe
- 8
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Homework Statement
i am given the equation of a parabola to be y=2x^2-2x+3 and asked to sketch the parabola
Homework Equations
y=1/2(l-p)(x-k)^2+(l+p)/2
(l+p)/2=h
vertex is at (k,h)
equation of the directrix is y=p
distance[(k,h) to y=p]=distance[(x,y) to (k,h)]
The Attempt at a Solution
(1) completing the squares for y=2x^2-2x+3 i get
y=2(x-1/2)^2+2
=>k=1/2 &
h=2 &
a=2
.'. vertex is at (1,2)
(2) (l+p)/2=h=2 ...eqn1
1/(2(l-p))=a=2...eqn2
making l the subject in eqn.1 i get
l=4-p
substituting in eqn2 i get
1/(2(4-p-p))=2
=>1/(8-4p)=2
=>1=16-8p
.'.p=-15/8~-1.08
=>eqn of directrix is y=-1
(3)given the vertex is at (1,2)
F is at (1,3) taking (1,-1) from the directrix
from (2,4) to F is sq. root of 2 units
from (2,4) to (1,-1) is sq. root of 26 units
AND THIS ISNT A PARABOLA
PLEASE, WHERE HAVE I WENT WRONG BUDDIES?!?