Question

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

Answer 1

@rishavraj

Answer 2

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

Answer 3

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

Answer 4

um -6 and 6

Answer 5

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

Answer 6

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

Answer 7

well... notice whre the vertex is at
the vertex is at (0, 36)

well.. actaully that's quite close, one sec

Answer 8

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

Answer 9

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.

Answer 10

\(\bf y=a(x-{\color{brown}{ h}})^2+{\color{blue}{ k}}
\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\)

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
\(\bf y=-ax^2+36\implies \cfrac{y-36}{-x^2}=a\implies \cfrac{0-36}{-6^2}=a\)

Answer 11

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

Answer 12

ohh yeah, it would, anyhow, kudos :)

Answer 13

lemme check the other bit

Answer 14

Thanks:) Because I have no idea what to do

Answer 15

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

Answer 16

Ok.

Answer 17

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

Answer 18

how did you get 1/3x+25?

Answer 19

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

Answer 20

I simply made sure the line was secant to the parabola

Answer 21

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

Answer 22

ok, so what would the points be?

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIteF4yKzM2IiwiY29sb3IiOiIjRTMxMjEyIn0seyJ0eXBlIjowLCJlcSI6IigxLzMpeCsyNSIsImNvbG9yIjoiIzIyMUJFMCJ9LHsidHlwZSI6MCwiZXEiOiI5LzV4KzIwIiwiY29sb3IiOiIjMTNFMzBDIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTI2LjMwNjMwNDkzMTY0MDYwNyIsIjIzLjI4NDc1OTUyMTQ4NDM1NyIsIjcuMzM0MjEzMjU2ODM1OTQ2IiwiMzcuODUxNzkxMzgxODM1OTMiXX1d

Answer 28

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

Answer 29

\(\begin{array}{rrllll}
x&y\\
\\\hline\\
-6&\frac{1}{3}\cdot -6+36\\
-4&\frac{1}{3}\cdot -4+36\\
-2&\frac{1}{3}\cdot -2+36\\
0&\frac{1}{3}\cdot 0+36\\
2&\frac{1}{3}\cdot 2+36\\
4&\frac{1}{3}\cdot 4+36\\
6&\frac{1}{3}\cdot 6+36\\
\end{array}\)

there, that'd a table for the blue one

Answer 30

yw

Answer 31

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

Answer 32

np