Question

Find the equation of the parabola.

Answer 1

So vertex form is

y=a(x-h)^2+k

(h,k) is the vertex
you can plug in the point given (x,y), and the vertex to solve for a

can you try?

Answer 2

ok wait up.

Answer 3

just curious, but does anyone know how to approach this some other way, its cause i was taught another way. Any suggestions?

Answer 4

Well close, you still need to plug in the point given for your x and y

4=a(2)^2
4=4a
a=1

so if a=1

y=1(x-0)^2+0

which can just be written as y=x^2

Answer 5

How i was taught anyway, sorry i dont know another way =p

Answer 6

since axis of symmetry is x-axis so and vortex at origin so
y^2=4ax

put x= 2 and y =4 to get a

Answer 7

well , it was evident from the given point (2,4 ) it must be to the right of the origin :)

Answer 8

from given information you decide it .

for example if points were (-2,4) then

y^2=4ax
16=4a(-2)
a=-2

and equation will be
y^2=-8x

Answer 9

because its the standard form
weather its -4ax or 4ax will be decided by sign of a once we find the a we can tell to which side it will be opening .

Answer 10

exactly
x^2=4ay!

Answer 11

ok post it will see :)

Answer 12

from the directrix line x=20 its ecident that parabola is symmetric about x -axis .
also direxrix is positive so the parabola is opening to the left
distanc between vortex and focus is equal to directrix so
vortx is at teh midway beetween focus and directrix
(focus is to th left of vortex and directrix so a must be negativ a=-20
so vortex must be at (0,0)no wthe eqaution will be
y^2=-4*20x
y^2=-80x

Answer 13

for the second one (since he y coordinate of both the focus and vortex are same so the parabola is symmetric about x axis)
distance between vorex and focus =a= 4
since vortex is to the left of the focus so the parabola is opening to the right side os the x axis

so
y^2=4*4x
y^2=16x

Answer 14

because always use the standard form
y^2=4ax
since a=-20 so
y^2=4(-20)(x)=-80x

Answer 15

its simple you know that it will be opening to the left side (becasue of he minus siagn )
take some values x=0,-1,-2,-3 get correcspopnding y points
plot theses point on paper
join them .

Answer 16

may be but i know taht is the simple way .