Question

Please help algebra 2

Answer 1

Tony is trying to find the equation of a quadratic that has a focus of (−1, 4) and a directrix of y = 8. Describe to Tony your preferred method for deriving the equation. Make sure you use Tony's situation as a model to help him understand.

Answer 2

first start with the vertex-form of a parabola, its:
y = a(x-h)^2 + k

next, solve for the vertex of the quadratic by using the value of the focus and the directrix.
since, the focus is: (-1, 4) and
the direxrix is: y=8

use the mid point formula from the focus to the directrix to find the y-value of the vertex.

the x-value of the vertex will be the same as the x-value in the focus, -1

so at this point, we will have the values of the vertex, (h, k).
plug those into the equation.


all that is left to find is the value for 'a'

Answer 3

Would the midpoint be -0.5/ 2?

Answer 4

@DemolisionWolf

Answer 5

hmm.... maybe it would be easier if I showed it this way:

where is the midpoint for this number line, given the two points, i circle?

Answer 6

the midpoint would be 6

Answer 7

@DemolisionWolf

Answer 8

yep!

Answer 9

so we know that the vertex of the parabola is (h, k) or (-1, 6)
plug those into the equation:
y = a(x-h)^2 + k

Answer 10

y = a(-1 - 6)^2 + k?

Answer 11

close!!
(h, k) is (-1, 6)
so,
h = -1
k = 6

try again ^_^ once more

Answer 12

y = a(x- (-1))^2 + 6

Answer 13

yep, thats right

Answer 14

so, two more steps, the next step is to figure out what 'a' is. then once we have that, we expand the equation we have been 'making'

Answer 15

Could you keep explaining how to solve? I know I may be frustrating you but I really do want a good grade in my class.

Answer 16

yea, i can do that

Answer 17

do you have any question about why i've done the steps I have so far?

Answer 18

Nope, I think I've gotten it. I'm writing it down on a sheet of paper and following along :)

Answer 19

@DemolisionWolf

Answer 20

cool

Answer 21

so the next step was to find 'a'

'a' is the distance from the vertex (-1, 6) to the focus (-1, 4)

can you tell me what that distance is?

Answer 22

12?

Answer 23

@DemolisionWolf

Answer 24

try again ^_^

Answer 25

Would it be -1, 5? or just 5? I used the distance formual to get 12 lol

Answer 26

@DemolisionWolf

Answer 27

did u get my message i sent? a=-2