A water taxi travels around an island in a path that can be modeled by the equation y = 0.5(x - 10)². A water skier is skiing along a path that begins at the point (8, 2) and ends at the point (14, 8). Write the linear equation that models the path of the skier.

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dnwilliams838

19.02.2022

Mathematics

You start with the equations:

$y = -x^{2} - 4x$ and y = 2x +5

Then you say y = y, then $-x^{2} - 4x = 2x + 5$

now you want to put all your numbers in one side of the equation and combine like terms in that side of the equation.

$2x + 5 +x^{2} +4 x = 0$

$(2x + 4x) + x^{2} + 5 = 0$

$x^{2} + 6x + 5 = 0$

And now you have a quadratic equation, where you can determine the value of x using the Bhaskara method.

$x = \frac{-6 +-\sqrt{6^{2} - 4*5 } }{2} = -3+- \frac{\sqrt{36 - 20} }{2} = -3+- \frac{\sqrt{16} }{2} = -3+- 2$

Then your solutions are x = -1 and x = -5.

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