Create an equation.

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Create an equation.

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I think I got the equation but not the second part. y=-x^2+36
Would i be right?
the vertex form is- a(x -b)^2 + c so here we have y = -a(x - 0)^2 + 36
when y = 0 x = 6 0 = -a(6)^2 + 36 so a = 1 equation is y = -x^2+ 36
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.
its negative before the x^2 because the parabola opens downwards
this is the second part which i don't understand that goes with this equation :(
well it a matter of picking a sloped line and choosing which points you want it to intersect the parabola
Ok so which points should I choose? Actually, I'll let you decide.
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.
x = -5 y = -(-5)^2 + 36 x = 4 y = -(4)^2 + 36
so y=41 and y=32 ??
so thats 2 values for your linear function
now what do I do?
What would the table look like?
hmm - i wonder if this is easiest way to do this - anyway we've started it this way so we may as well continue
i've done things wrong way round...
Is that a 6?
scrap all that and build the table first - that's what they asked for anyway
What do you mean?
No matter, we can always start over:)
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
so thats 2 values on our table
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
-x^2 + 36 = x + 10 x^2 + x - 26 = 0
What what would the table look like?
- yes - thats what we are calculating now
you can solve this by using quadratic formula
Oh sorry!
there will be 2 values for x you can find the correspondimg values of y by subbing in y = x + 10
Ok! I see :)
|dw:1438212449020:dw|
Alright:)
so then we would need 2 more points correct?
just to check, these are 2 points of intersection?
yes solve the quadratic for x theh y = x +10 for the 2 values
* 2 y values
yes
ok! But where did the y=x+10 come from?
the first x value will be between -6 and -5 and second will be between 4 and 5
x = (-1 +/- sqrt(1^1 - 4*1*-26)) / 2
ok, so it could be like -4 for the first and idk for the second
alright :)
that comes to x = 4.62 and - 5.62
gtg right now
u still there?

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