Question

Please help?? Check my answer! Will medal!
A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base, as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is seventy four feet and its width from left to right is twenty eight feet.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Answer 1

@zepdrix @Luigi0210 Please help!! Check my work?

Answer 2

-74 = -a(14)^2 b(14)
-74 = -a (-14)^2 b(-14)

-74=196a-14b and
-74=196a 14b

Im not sure what to do next or if thats correct?

Answer 3

@tkhunny please check my work

Answer 4

@RhondaSommer

Answer 5

oml

Answer 6

@RhondaSommer did I start off right?

Answer 7

i was horrible with these. as much id love to help you; I would probably do more hurt then help. sorry :(

Answer 8

thats okay! Thanks for trying! Hopefully someone will help because Im super confused @RhondaSommer

Answer 9

Personally, I'd move it up 74 ft, but that is of no consequence. It should still work.

Opening Down - General Form

4p(y-k) = (x-h)^2 and p < 0

You have your vertex at (0,0).

4py = x^2 and p < 0

You have two points (14,-74), (-14,-74)

4p(-74) = 14^2 ==> p = -0.6621621622

That's about it.

Answer 10

at least i didnt try and give you the wrong answer XD that would have been BAAAAD

Answer 11

You're awesome, Rhonda. Keep trying. Better every day. :-)

Answer 12

@tkhunny is that all I have to do? they ask for the equation of the parabola

Answer 13

@Luigi0210 what do you think?

Answer 14

Nope, the last thing you have to do is ignore me a little. I see the problem statement TOLD you to put the vertex at the origin.

Is that the equation or not? Knowing when you are done is important.

Answer 15

I think that the equation in that case would be -2.648y=x^2 when you plug p in. Is that it? @tkhunny

Answer 16

@Qwertty123

Answer 17

hm...

Answer 18

@Qwertty123 What do you think?

Answer 19

@IrishBoy123

Answer 20

Here:
y = ax^2 + bx + c

Use (0, 0):
0 = a(0^2) + b(0) + c
c = 0

Use (-14, -74)
-74 = a(-14)^2 + b(-14)
196a -14b = -74

Use (14, -74)
-74 = a(14)^2 + b(14)
196a + 14b = -74

Solve the system of equations by addition:
196a -14b = -74
196a + 14b = -74

392a = -148
a = -148/392 = -37/98

196(-37/98) + 14b = -74
14b = 0
b = 0

y=?

Answer 21

listen to tkh :-)))

Answer 22

did he finish it or do I need to do more @IrishBoy123

Answer 23

You are right @IrishBoy123

Answer 24

Im not sure of how to see what equals y @Qwertty123

Answer 25

whoops I think I wrote the answer! :/

Answer 26

what do you mean? @Qwertty123 what do I need to end up with?

Answer 27

oh would it be y= -37/98x^2

Answer 28

@Qwertty123

Answer 29

Yes it would be! :D

Answer 30

How come thats not what tkh got @Qwertty123

Answer 31

subtract them together you have -28b =0 which give you b =0
then -74 =196 a -14*0 --> a = −74196=−3798
Now, you have a =−3798 , b =0, c=0
the parabola form is y=−37/98x^2

Answer 32

I don't know! Sorry But that is how

Answer 33

oh okay thanks so much!

Answer 34

You welcome! :D

Answer 35

@IrishBoy123 do you agree?