Please help me with my Algebra 2??? what is an equation of a parabola with the given vertex and focus vertex:(-2,5) focus:(-2,6) someone PLEASE help me :(

Question

anonymous · Answer

do you remember the standard formula

jim_thompson5910 · Answer

the distance from vertex to focus is 1 unit, so p = 1

the vertex is (-2,5), so (h,k) = (-2,5) ---> h = -2, k = 5

4p(y-k) = (x-h)^2

4*1(y-k) = (x-h)^2

4*1(y-5) = (x-(-2))^2

4*1(y-5) = (x+2)^2

y-5 = (1/4)(x+2)^2

I'll let you finish up

anonymous · Answer

I don't really know what to do

jim_thompson5910 · Answer

you would solve for y and get it into vertex form or standard form (depending on what your teacher wants)

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

standard form is y = ax^2 + bx + c

jim_thompson5910 · Answer

what do you get when you do this?

anonymous · Answer

Do I add 5 to both sides?

jim_thompson5910 · Answer

yes that will get the equation into vertex form

jim_thompson5910 · Answer

if necessary, you'll have to convert it to standard form

anonymous · Answer

I don't understand what to do after that

anonymous · Answer

As you can tell math is NOT my strong suit

anonymous · Answer

And I also have no idea how to find the focus

jim_thompson5910 · Answer

the focus is given to you, in this case it's (-2,6)

jim_thompson5910 · Answer

if you add 5 to both sides, you get

y-5 = (1/4)(x+2)^2

y = (1/4)(x+2)^2+5

then you would expand out (x+2)^2, distribute the 1/4, then combine like terms

anonymous · Answer

y = (1/4)(x+2)^2+5? Is that the answer?

jim_thompson5910 · Answer

that's the answer in vertex form

jim_thompson5910 · Answer

if that's what they want, you can stop there

anonymous · Answer

So do I multiply by 4 to cancel the fraction?

jim_thompson5910 · Answer

what do you get when you expand out (x+2)^2

anonymous · Answer

It just wants the equation of the parabola

anonymous · Answer

2x+4?

jim_thompson5910 · Answer

(x+2)^2 = (x+2)(x+2) = ???

anonymous · Answer

Or x^2+4

jim_thompson5910 · Answer

closer, but it's really x^2 + 2x + 4

jim_thompson5910 · Answer

oops i meant x^2 + 4x + 4

jim_thompson5910 · Answer

so 

y = (1/4)(x+2)^2+5

turns into

y = (1/4)(x^2 + 4x + 4) + 5

anonymous · Answer

I kinda understand the math, but I don't know what the equation is? Do I use the vertex form?

jim_thompson5910 · Answer

then you distribute the 1/4 through to get 

y = (1/4)(x^2 + 4x + 4) + 5

y = (1/4)x^2 + (1/4)*4x + (1/4)*4 + 5

y = (1/4)x^2 + x + 1 + 5

now combine like terms to get this

y = (1/4)x^2 + x + 6

anonymous · Answer

So is that my equation?

anonymous · Answer

Thank you very very much for your help