## anonymous one year ago An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix (8). d = (square root) (Xv2 - 3)^2 + (Yv2 - 6)^2 d = (square root) (Yv2 - 8)^2 I need to something like -1/-8x^2 + 5/4x + 23/8 = y (example given by school) Its to do an arc. I got to Xv2^2 -6Xv2 + 9 + Yv2^2 -8Yv2 + 16 = ???

1. anonymous

You are forgetting the weird exponent that is below the number. I don't know if that effects the equation at all though. What I'm supposed to get is something like $-\frac{ 1 }{ 8 } x^2 + \frac{ 5 }{ 4 } x + \frac{ 23 }{ 8 } = y$ Which someone how becomes this -0.13x^2 + 1.25x + 2.88 (Not my problem, its their example)

2. anonymous

Expand it? And give me a second, I'll stitch together some screenshots of what they gave for instructions.

3. anonymous

4. anonymous

I don't really understand any of this as I was horrible at algebra. I need it like what I said before, "-0.13x^2 + 1.25x + 2.88" so I can put it in stupid geogebra to submit for my project.

5. anonymous

Because I have to put it into geogebra, or I don't get a grade.

6. campbell_st

so let's check... the focus is at (3, 6) and directrix is at y = 8

7. anonymous

yes

8. campbell_st

great so using the distance formula method pick a point P(x, y) on the parabola distance Focus to P $d = \sqrt{(x - 3)^2 + (y - 6)^2}$ P to the directrix $d = \sqrt{x -x)^2 + (y - 8)^2}$ equating and squaring you get $(x -3)^2 + (y - 6)^2 = (y - 8)^2$ now subtract (y - 6)^2 from both sides $(x -3)^2 = (y -8)^2 - (y -6)^2$ does that make sense..?

9. campbell_st

so simplify the right hand side $(x-3)^2 = y^2 - 16y + 64 - y^2 + 12y - 36$ which becomes $(x -3)^2 = -4y + 28$ factor the right hand side $(x -3)^2 = -4(y - 7)$ does that make sense...?

10. campbell_st

make y the subject $-\frac{(x -3)^2}{4} + 7 = y$ you can enter the equation as its written above into Geogebra...

11. campbell_st

it will then write the equation in expanded form with decimal coefficients...

12. campbell_st

and I just graphed the parabola in geogebra and it worked perfectly...

13. anonymous

how do you graph it in it?

14. campbell_st

just enter the equation I've written above $y = -\frac{(x -3)^2}{4} + 7$

15. anonymous

y = -0.25x^2 + 1.5x + 4.75?