Question

Write the equation in standard form for the parabola. vertex (6,8) contains the point (4,-2) axis of symmetry x=6

Answer 1

little help @jhannybean

Answer 2

first get all the information given into an equation of a parabola
doesn't matter which form for the first step
can you do that? :)
@rislam21

Answer 3

hint: vertex form for a parabola is y = a(x - h)^2 + k
when (h , k) is the vertex

Answer 4

Okay so I think that this parabola is going down, meaning it will be in the y-k=1/4p (x-h)² form and by using the coordinates of the vertex, the equation is now y-8=1/4p (x-h)² the problem is that I don't know how to get the value of p to finish the equation.

Answer 5

(x-6)²**** sorry

Answer 6

hmmm
I suggest plugging in the vertex first to get
y = a (x - 6)^2 + 8
then to temporarily plug in the point (4, -2) for (x, y) to solve for a

Answer 7

is this it: y= -14(x-6)² +8

Answer 8

hmmmm
-2 = a (4 - 6)^2 + 8
can you solve for a from there? :/

Answer 9

does a equal -2.5

Answer 10

yes! :D
so plug a = -2.5 into y = a (x - 6)^2 + 8

Answer 11

y= -2.5(x-6) ² +8 then y= x ² -12x +33.5

Answer 12

mmmm
(x - 6)^2 = (x-6)(x-6) = x^2 - 12x + 36
-2.5(x^2 - 12x + 36) --> -2.5x^2 + 30x - 90 + 8 = ?

Answer 13

ohh ok -2.5x ² +30x -82

Answer 14

yes! :D
tahdahhh

Answer 15

wait no that cant be the answer to my question because the standard form for a parabola where the vertex is not at the origin is in the form x-h=1/4p (y-k) ² if the parabola is going left or right and y-k=1/4p(x-h) ² if the parabola is going up or down

Answer 16

ohhhh ok whoops sorry >,<
I haven't dont conics in a long time :/
axis of symmetry is x = 6 so going up or down
so use y - k = 1/4 p(x - h)^2
plug in the vertex (6, 8)
then do what we did before to try to solve for p?

Answer 17

no problem! yea I don't know how to solve for P this is all I could do y-8=1/4p x^2 -12x +36 I don't know what to do next:(

Answer 18

good :)
I think you should temporarily plug in the point (4 ,-2) for (x , y) to solve for p

Answer 19

ahould I plug 4 into x^2 so that is become 16?

Answer 20

yes :)

Answer 21

I got up to this: -14= 1/4p what do I do next? Should I divide both sides by 1/4?

Answer 22

multiply both sides by 4

Answer 23

p= -56

Answer 24

actually...
-2 - 8 = 1/4 p (16 - 48 + 36)
-10 = 1/4 p (4)
-10 = p

Answer 25

Oh so the equation would be y-8= -1/40 (x-6)^2 ?

Answer 26

-10/4 = -5/2
y - 8 = -5/2 (x-6)^2

Answer 27

wait how did you get -5/2

Answer 28

(1/4)p
p = -10
(1/4) (-10) = -10/4

Answer 29

Ohh okie dokie thanks so much for your help!!!!!!!!!!!!!

Answer 30

:)

Answer 31

cool