Question

Put into standard form. x^2 + 8x - 10y - 34 = 0 (parabola)

Answer 1

I have gotten to this.

(x+4)^2 = 10y+18. im not sure what o do next

Answer 2

\[y=0.1x ^{2}+0.8x-3.4\]

Answer 3

im looking for the form (x-h)^2 = 4p (x-h)

Answer 4

ooooooh ,yes

Answer 5

\[(x+4)^{2}=10(y+1.8)\]

Answer 6

Thats what i got, but what would be the vertex?

Answer 7

(-4,-1.8) i would assume. If thats rigtht then none of my options are correct :/

Answer 8

sorry is not correct
\[(x+4)^{2}=10(y+4.2)\]
is it true?

Answer 9

the options are (-4,-5) (-4,5) (-4,3.4)

Answer 10

im sorry i Mixed up ....
\[(x+4)^{2}=10(y+5)\]
i sure that is right :)

Answer 11

Ok thank you. Could you please tell me how you got there?
just a quick explanation

Answer 12

@fazeli u a girl ;)

Answer 13

nice and cute name ;)

Answer 14

haye itna na tarsao jaldi type karo my fazeli ;)

Answer 15

thanks
you started the question, i only Simplify Phrase.

Answer 16

thanks anyway..

Answer 17

\[x^2 + 8x - 10y - 34 = 0\]Move all terms not containing \(x\) to the right side to get them out of the way while we complete the square:
\[x^2+8x = 10y+34\]Complete the square by adding half the coefficient of the \(x\) term, squared, to both sides:
\[x^2+8x+(\frac{8}{2})^2 = 10y+34 + (\frac{8}{2})^2\]\[x^2+8x + 16 = 10y+34 + 16\]Rewrite left hand side as a perfect square:\[(x+4)^2 = 10y+34+16\]\[(x+4)^2 = 10y+50\]Factor right hand side\[(x+4)^2 = 10(y+5)\]\[10=4p\]\[p=\frac{5}{2}\]Standard form is \[(x+4)^2 = 10(y+5),\text{ with }p=\frac{5}{2}\]
Standard form gives us \[(x-h)^2 = 4p(y-k)\]
\[x+4 = x-h\]\[h=-4\]\[y+5=y-k\]\[k=-5\]Vertex is at \((h,k) = (-4,-5)\)

You can check this result by putting equation in vertex form:
\[y = a(x-h)^2+k\]\[(x+4)^2 = 10(y+5)\]\[(x+4)^2=10y+50\]\[10y=(x+4)^2-50\]\[y=\frac{1}{10}(x+4)^2-5\]Again, \(h = -4, \,k = -5\) so our original vertex of \((-4,-5)\) was correct.

Answer 18

Here's a plot of the parabola between \(x=-15\) and \(x = 10\) showing the vertex at \((-4,-5)\)

Answer 19

THANK YOU SO MUCH :D!!! fan

Answer 20

@whpalmer4 U a girl!!! =D ?

Answer 21

uh, no :-) what gives you that idea?

Answer 22

HahA :D

Answer 23

I'd make quite the attractive girl — I can cover my eyes with my beard :-)

Answer 24

WAH WAH :D what a special type of beard!!YOU GO BRO!!!

Answer 25

I'm saving a bundle not buying razor blades :-)

Answer 26

a few hundred years of razor blade savings and I'll be able to buy a used Harley to go with the beard :-)