itsmichelle29
  • itsmichelle29
Create an equation. Use the graph below to create the equation of the rainbow parabola.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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itsmichelle29
  • itsmichelle29
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Michele_Laino
  • Michele_Laino
since your parabola is symmetric with respect to the y-axis, then its equation is like below: \[\Large y = a{x^2} + b\] where a, and b are two coefficients to be determined
itsmichelle29
  • itsmichelle29
okay

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itsmichelle29
  • itsmichelle29
How do i solve
Michele_Laino
  • Michele_Laino
now since your parabola passes at point (6,0) I substitute into the above equation x=6 and y=0, so I get: \[0 = a{6^2} + b = 36a + b\] am I right?
itsmichelle29
  • itsmichelle29
IDK
itsmichelle29
  • itsmichelle29
=(((((
itsmichelle29
  • itsmichelle29
no your not i check you equation onilne
Michele_Laino
  • Michele_Laino
if I susbstitute x=6 and y=0, into my equation I get: |dw:1436731567990:dw|
Michele_Laino
  • Michele_Laino
I think that I'm right, since it is a simple substitution
Michele_Laino
  • Michele_Laino
now, since your parabola passes at point (0,36), then the coordinates of that point have to make our equation as an identity. So please substitute x=0 and y= 36 into my equation above, what do you get?
Michele_Laino
  • Michele_Laino
|dw:1436731869598:dw|
Michele_Laino
  • Michele_Laino
hint: x=0, means x^2=x*x=0*0=0
itsmichelle29
  • itsmichelle29
36= ? +b
itsmichelle29
  • itsmichelle29
I dont understand
Michele_Laino
  • Michele_Laino
that's right! we have: 36=0+b or: 36=b
itsmichelle29
  • itsmichelle29
Okay so ?????
Michele_Laino
  • Michele_Laino
so, we got this algebraic system: \[\Large \left\{ \begin{gathered} 36a + b = 0 \hfill \\ \hfill \\ b = 36 \hfill \\ \end{gathered} \right.\] please solve for a and b Hint, we already know what is b, since b=36 from the second equation
Michele_Laino
  • Michele_Laino
please substitute b=36 into the first equation, wht do you get?
Michele_Laino
  • Michele_Laino
what*
itsmichelle29
  • itsmichelle29
-1
Michele_Laino
  • Michele_Laino
namely, you have to replace b with 36 into the first equation
Michele_Laino
  • Michele_Laino
perfect a=-1
Michele_Laino
  • Michele_Laino
now, substitute a=-1 and b=36 into this equation: \[\Large y = a{x^2} + b\] what do you get?
Michele_Laino
  • Michele_Laino
namely, replace a with -1 and b with 36
itsmichelle29
  • itsmichelle29
y=-1x^2+36
Michele_Laino
  • Michele_Laino
that's right! That it is your equation
campbell_st
  • campbell_st
look at the zeros of the parabola, or where it cuts the x-axis x = -6 and x = 6 the factors that produce these zeros are x + 6 = 0 and x - 6 = 0 so the parabola is y = a(x -6)(x+6) where a is a constant this distributes to y = a(x^2 - 36) now substitute to point (0, 36) to find a so 36 = a((0)^2 - 36) or 36 = -36a solve for a hope it helps
itsmichelle29
  • itsmichelle29
Okay thanks guys for your help
Michele_Laino
  • Michele_Laino
thanks! @itsmichelle29

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