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x= -.9309309

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The vertex of this graph is (88.381, 68.138). This is where the egg passes over Nate's head.

The y-intercept of the graph is (0, 27). This is the point from where Patrick throws the egg to Kate.

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Plug this equation into Y1 in your calculator and hit graph. Make sure your window is set to where you can see the parabola. To find the vertex, go to 2nd -> Trace -> Maximum. To find where the egg would have landed had Kate not been standing there to catch it (the zero), go to 2nd -> Trace -> Zero. To find how high in the air the egg was at a certain distance, go to 2nd -> Trace -> Value and plug in a distance. To find how far the egg had travelled once it reached a certain height, plug in the height (in Y2), hit Graph, then go to 2nd -> Trace -> Intersect.

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Plug these values into the standard quadratic form. The equation should look like this:

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Multiple the inverse of the first matrix with the second matrix. The resulting matrix should look like so:

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Set up a matrix with the corresponding y values. The matrix will look like so

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Set up a matrix with the coordinates presented in the problem: (0, 27), (83.25, 68), and (166.5, 36). The matrix will look like so:

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Kate, Nate, and Patrick are participating in an egg toss competition. Patrick tosses the egg from 27 inches off the ground and tosses it 166.5 inches to Kate, the egg barely gliding over Nate's luscious hair exactly in between Patrick and Kate. Nate stands at 5'8", and Kate catches the egg 36 inches off the ground. Write and graph a quadratic equation to demonstrate this situation.