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

1. anonymous

@rishavraj

2. anonymous
3. rishavraj

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

4. anonymous

um -6 and 6

5. rishavraj

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. 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.

10. anonymous

$$\bf y=a(x-{\color{brown}{ h}})^2+{\color{blue}{ k}} \qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})$$ 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 $$\bf y=-ax^2+36\implies \cfrac{y-36}{-x^2}=a\implies \cfrac{0-36}{-6^2}=a$$

11. anonymous

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

12. anonymous

ohh yeah, it would, anyhow, kudos :)

13. anonymous

lemme check the other bit

14. anonymous

Thanks:) Because I have no idea what to do

15. anonymous

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

16. anonymous

Ok.

17. anonymous

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

18. anonymous

how did you get 1/3x+25?

19. anonymous

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

20. anonymous

I simply made sure the line was secant to the parabola

21. anonymous

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

22. anonymous

ok, so what would the points be?

23. anonymous

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

24. anonymous

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

25. anonymous

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

26. anonymous

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

27. anonymous
28. anonymous

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

29. anonymous

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

30. anonymous

yw

31. anonymous

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

32. anonymous

np