Question

100 POINTS!!!! 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 for at least four values for the function. Remember to include the two points of intersection in your table. Can you just give me the X and Y values?

Answer 1

Based on the docx you showed me, the equation for the parabola is $y = x^2 + 36$ and you want a table of values for a linear equation that intersects the parabola at (5, 6) and (-2, 34).

If you use these two points to create a line we get the equation:

$y - 6 = \frac{34 - 6}{-2 - 5}(x - 5)$ (I just used point slope form)

This can be simplified to:

$y = \frac{40}{-7}x + \frac{242}{7}$

Now we just need to create a table of points on this line. We already have the points you gave and we can also use the y-intercept: $(0, \frac{242}{7})$ and the x-intercept: $(\frac{121}{20}, 0)$.

So our table of value can be:

x          | y
______|________
-2         | 34
0          | 242 / 7
5          | 6
121/20 | 0

Answer 2

So I'm guessing the answer is: any x from -6 to 6; any absolute value > 6 is not meaningful in this case because the x-axis represents the ground level, and no y values can be negative (underground). Range: y values from 0 (ground) up to 36 (an upward measure, in some kind of units). Drone flying upward is y = mx+b; choose m > 0 and b > 0 (e.g. m = 0.5, b = 24)--this will intersect the rainbow twice; you can find those points of intersection by setting the y values of line & parabola =, and solving the resulting quadratic equation by using the quadratic formula. x values of intersection are about -3.60 and 3.35.