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itsmichelle29
 one year ago
Create an equation. Use the graph below to create the equation of the rainbow parabola.
itsmichelle29
 one year ago
Create an equation. Use the graph below to create the equation of the rainbow parabola.

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1since your parabola is symmetric with respect to the yaxis, then its equation is like below: \[\Large y = a{x^2} + b\] where a, and b are two coefficients to be determined

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now 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
 one year ago
Best ResponseYou've already chosen the best response.0no your not i check you equation onilne

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1if I susbstitute x=6 and y=0, into my equation I get: dw:1436731567990:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that I'm right, since it is a simple substitution

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1436731869598:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: x=0, means x^2=x*x=0*0=0

itsmichelle29
 one year ago
Best ResponseYou've already chosen the best response.0I dont understand

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1that's right! we have: 36=0+b or: 36=b

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so, 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
 one year ago
Best ResponseYou've already chosen the best response.1please substitute b=36 into the first equation, wht do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1namely, you have to replace b with 36 into the first equation

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, substitute a=1 and b=36 into this equation: \[\Large y = a{x^2} + b\] what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1namely, replace a with 1 and b with 36

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1that's right! That it is your equation

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0look at the zeros of the parabola, or where it cuts the xaxis 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
 one year ago
Best ResponseYou've already chosen the best response.0Okay thanks guys for your help

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1thanks! @itsmichelle29
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