Create an equation.

- anonymous

Create an equation.

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- anonymous

@Michele_Laino

- anonymous

@Hero

- anonymous

@welshfella

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## More answers

- anonymous

http://assets.openstudy.com/updates/attachments/556f231ce4b0c4e453fa9e42-rosebud4612flvs-1433346859795-1.gif

- anonymous

I think I got the equation but not the second part. y=-x^2+36

- anonymous

Would i be right?

- welshfella

the vertex form is- a(x -b)^2 + c
so here we have
y = -a(x - 0)^2 + 36

- welshfella

when y = 0 x = 6
0 = -a(6)^2 + 36 so a = 1
equation is y = -x^2+ 36

- 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.

- welshfella

its negative before the x^2 because the parabola opens downwards

- anonymous

this is the second part which i don't understand that goes with this equation :(

- welshfella

well it a matter of picking a sloped line and choosing which points you want it to intersect the parabola

- anonymous

Ok so which points should I choose? Actually, I'll let you decide.

- welshfella

pick the point where x is -5 and x = 4
you can work out the value of y by plugging these values into the equation.

- welshfella

x = -5 y = -(-5)^2 + 36
x = 4 y = -(4)^2 + 36

- anonymous

so y=41
and y=32
??

- welshfella

so thats 2 values for your linear function

- anonymous

now what do I do?

- anonymous

What would the table look like?

- welshfella

hmm - i wonder if this is easiest way to do this - anyway we've started it this way so we may as well continue

- welshfella

i've done things wrong way round...

- anonymous

Is that a 6?

- welshfella

scrap all that and build the table first - that's what they asked for anyway

- anonymous

What do you mean?

- anonymous

No matter, we can always start over:)

- welshfella

let the equation of the line be y = x + 10
pick 2 values for x either side of -6 and +6
lets work these 2 points out
x = -7 y = -7 + 10 = 3
x = 8 y = 8 + 10 = 18

- welshfella

so thats 2 values on our table

- welshfella

no we need to find the 2 points of intersect on the rainbow
we can do this by solving the system of equations
y = x + 10
y = -x^2 + 36

- welshfella

-x^2 + 36 = x + 10
x^2 + x - 26 = 0

- anonymous

What what would the table look like?

- welshfella

- yes - thats what we are calculating now

- welshfella

you can solve this by using quadratic formula

- anonymous

Oh sorry!

- welshfella

there will be 2 values for x
you can find the correspondimg values of y by subbing in y = x + 10

- anonymous

Ok! I see :)

- welshfella

|dw:1438212449020:dw|

- anonymous

Alright:)

- anonymous

so then we would need 2 more points correct?

- anonymous

just to check, these are 2 points of intersection?

- welshfella

yes solve the quadratic for x
theh y = x +10 for the 2 values

- welshfella

* 2 y values

- welshfella

yes

- anonymous

ok! But where did the y=x+10 come from?

- welshfella

the first x value will be between -6 and -5 and second will be between 4 and 5

- welshfella

x = (-1 +/- sqrt(1^1 - 4*1*-26)) / 2

- anonymous

ok, so it could be like -4 for the first and idk for the second

- anonymous

alright :)

- welshfella

that comes to x = 4.62 and - 5.62

- welshfella

gtg right now

- anonymous

u still there?

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