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.

days of the week

step-by-step explanation:

javier earned more money then kyle, so that won't always be a constant term, but the days of the week do not change so that term is always constant.

edit: i meant

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."