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

- anonymous

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

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- chestercat

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- anonymous

@rishavraj

- anonymous

http://assets.openstudy.com/updates/attachments/557704cee4b03f31cab31848-maryslater-1433863506866-06_05_06_012.gif

- rishavraj

so wht do u thiink wht r the roots of the equation???

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## More answers

- anonymous

um -6 and 6

- rishavraj

cool......xD means u don't need any help :))

- anonymous

lol! I so I got -x^2+36 ??

- jdoe0001

well... notice whre the vertex is at
the vertex is at (0, 36)
well.. actaully that's quite close, one sec

- anonymous

and there's a 2nd part that I'm not understading

- anonymous

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.

- jdoe0001

\(\bf y=a(x-{\color{brown}{ h}})^2+{\color{blue}{ k}}
\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\)
the parabola is upside-down, meaning the "a" is negative, yes
thus \(\bf y=a(x-{\color{brown}{ h}})^2+{\color{blue}{ k}}
\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})
\\ \quad \\
y=-a(x-0)^2+36\implies y=-ax^2+36\)
we know the roots, thus, when y =0 , x = 6 or -6, let's use 6
so 6, 0 then
\(\bf y=-ax^2+36\implies \cfrac{y-36}{-x^2}=a\implies \cfrac{0-36}{-6^2}=a\)

- anonymous

Yes, so it would be -x^2+36 :)

- jdoe0001

ohh yeah, it would, anyhow, kudos :)

- jdoe0001

lemme check the other bit

- anonymous

Thanks:) Because I have no idea what to do

- jdoe0001

well, is a system of equations
lemme see if hmmm lemme graph it

- anonymous

Ok.

- jdoe0001

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIteF4yKzM2IiwiY29sb3IiOiIjRTMxMjEyIn0seyJ0eXBlIjowLCJlcSI6IigxLzMpeCsyNSIsImNvbG9yIjoiIzIyMUJFMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0xMy40MjQ4MzUyMDUwNzgxMTgiLCIxMS45NjU3ODk3OTQ5MjE4NjgiLCIyMS4xMDg2MjczMTkzMzU5MzgiLCIzNi43MzM2MjczMTkzMzU5MyJdfV0-
you have the "rainbow" parabola
and then you're asked to make a LINEar function
you're expected to use a table of values for the linear one
and to include at least, four values, more is fine
so if you use 10 values is ok as well, but not less than 4 values for the table
notice the graph.... the LINEar equation graph, crosses the parabola at two points

- anonymous

how did you get 1/3x+25?

- jdoe0001

made up :), you're expected to make one up, thus

- jdoe0001

I simply made sure the line was secant to the parabola

- jdoe0001

but you can cross the parabola by other lines as well
you could simply pick two points, to make a line
one on the left, one on the right
make sure they "cut" the parabola through, so they touch it at two points
and with two points you can get the equation of that line
from there you can get more values for the table

- anonymous

ok, so what would the points be?

- jdoe0001

well.. let's use the 1/3x + 25
one sec

- anonymous

why couldn't we use like 9/5x+20 or 2x+27? And okay, ill wait:)

- jdoe0001

either one will work, so long they "cut through" the parabola

- anonymous

okay:) So 9/5x+20 would cut through right?

- jdoe0001

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIteF4yKzM2IiwiY29sb3IiOiIjRTMxMjEyIn0seyJ0eXBlIjowLCJlcSI6IigxLzMpeCsyNSIsImNvbG9yIjoiIzIyMUJFMCJ9LHsidHlwZSI6MCwiZXEiOiI5LzV4KzIwIiwiY29sb3IiOiIjMTNFMzBDIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTI2LjMwNjMwNDkzMTY0MDYwNyIsIjIzLjI4NDc1OTUyMTQ4NDM1NyIsIjcuMzM0MjEzMjU2ODM1OTQ2IiwiMzcuODUxNzkxMzgxODM1OTMiXX1d

- anonymous

Thank you:)! And to find the points, we could just plug in numbers? or does it have to be specific

- jdoe0001

\(\begin{array}{rrllll}
x&y\\
\\\hline\\
-6&\frac{1}{3}\cdot -6+36\\
-4&\frac{1}{3}\cdot -4+36\\
-2&\frac{1}{3}\cdot -2+36\\
0&\frac{1}{3}\cdot 0+36\\
2&\frac{1}{3}\cdot 2+36\\
4&\frac{1}{3}\cdot 4+36\\
6&\frac{1}{3}\cdot 6+36\\
\end{array}\)
there, that'd a table for the blue one

- jdoe0001

yw

- anonymous

Yayyy! :) Lol I finally got it:) Thanks so muchhh

- jdoe0001

np

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