A penguin starts on a slide 3 feet above the water. He slides down and glides underwater. The function y=x^2-4x+3 shows his path where y is his height above or below the water, in feet, and x is the horizontal distance. Complete the square to find the interpret the extreme value (vertex).

( 2 , -1 )

Step-by-step explanation:

Given:-

A penguin starts on a slide 3 feet above the water. He slides down and glides underwater. The function of penguin height above/below the water is given  by:

                                    y = x^2 - 4x + 3

Find:-

-The extreme value (vertex) of the parabolic path

Solution:-

- The vertex ( turning point - minima or maxima ) can be evaluated by taking the first derivative of the given function and setting it equal to zero.

                                  dy/dx = 2x - 4

                                   0 = 2x-4

- Then solve for the critical value of function "x":

                                   x = 4/2 = 2 ft

- The vertex can be evaluated by substituting the critical value of "x" back into the function and evaluate for y:

                                  y = (2)^2 -4*2 + 3

                                  y = 4 - 8 + 3

                                  y = -1 ft

- The vertex of parabolic path lies at the coordinates ( 2 , -1 ). That is 2ft horizontal and 1 ft under water.

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