Create an equation. Use the graph below to create the equation of the rainbow parabola.

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Create an equation. Use the graph below to create the equation of the rainbow parabola.

Mathematics
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it's an upside down parabola
http://assets.openstudy.com/updates/attachments/556f231ce4b0c4e453fa9e42-rosebud4612flvs-1433346859795-1.gif

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what is the vertex-form of a parabola?
um... (h,k) is the vertex
y=a(x-h)^2-k @Loser66 ??
yes, but +k, not -k and your vertex is ???
(0,36)
ok, so, it is ?? y = ??
replace h, k in
um...y=x^2+36?
where is your a??
y =a x^2 +36 , ok??
kk!
Now, pick a point on the graph. (either of them, not vertex)
um -6?
a point means (.., ...) not just -6
(0,6)
you don't have that point!! , you have (-6,0) or (6,0)
which one do you choose??
whoops! um...(6,0) :)
ok, that is x =6 , y =0 right? plug that point into y = ax^2 +36, what do you have?
an upside down parabola / like a rainbow means the value of a is negative
y=-x^2+36
@triciaal please, be patient, it will be there!!
|dw:1437949718632:dw|
that is 0 = a*36 +36 , right?
-36 both sides, what do you get?
-y=x2-36
no!! redo 0 = a*36 +36 -36 -36 ---------------- ??
-36=a(0)
nope!! redo, please.
-36=36a
\(0= a*36 \cancel{+36}\\-36~~~~~~~\cancel{-36}\)
YYYYYYYYYYYYes!!
now, divided both sides by 36 , what do you get?
\(-36 = a*36\\\div 36~~~~~~\div 36\)
-1=a
yes !!yes!! yes!!!
:) Thanksss
Now, replace a =-1 into the vertex form y = ax^2 +36, you have????
ah! You would get...y=-1x^2+36
Binnnnnnnnnnnnnnnnngo!! you got it!! can write as y = -x^2 +36
yay!!!!!
@triciaal don't worry about parabola up or down. Apply the standard form, if it is up, we will get a >0, if it is down, we will get a<0.
Wait! Lol we have 1 more part that I don't understand. It's like Part 2 to the question
Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.
Any ideas??
hahaha... that is supposed to be my question, not yours.
since it is a linear function, that is a line, whatever you like, just "create" it. If I pick y = -x, then the line is |dw:1437950415171:dw|
It will "cut" the parabola at 2 points. |dw:1437950461903:dw|
If you pick y =x, it is perfectly ok, the line will be here and cut the parabola at 2 points like |dw:1437950524706:dw|
and the simplest case is |dw:1437950561325:dw|
still cut the parabola at 2 points. hehehe...
but where would the 2 points intersect?
but you must choose y =x, since the drone is upward, right?
|dw:1437950672718:dw|
Now, solve for the points you have y =x and y = -x^2 + 36 replace y =x x = -x^2 + 36 +x^2 both sides, what do you have?
But how would we "create a table of at least four values for the function. Remember to include the two points of intersection in your table?"
x^2+36
nope, redo.
x^2=x^2+36 ?
\(~~~~~~x = -x^2 +36\\+x^2~~~~+x^2\)
x+X^2=36
yes, now -36 both sides
\(x^2+x-36 =0\) right?
solve this quadratic, what do you get for x??
ok, I put it on my calculator and it gives me x = 5.52 and x = -6.52
um...I agree :)
Take them, now we have the line y =x, and those x values are the intersection of the line and the parabola The Table is just |dw:1437951089610:dw|
Thanks! You're really smart!
not that!! hehehe... just study the stuff before you.
haha! either way, you're awesome :)))

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