Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length of the horizontal chord of the parabola that has one end at (2/3, 1) .

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola:  

Part 1

If the curve passes through point , this means that when ,

Substitute these values into the equation and solve for :

Apply the exponent rule :

Part 2

We are told that one end of the chord is at and that the chord is horizontal.  Therefore, the y-coordinate of the other end of the chord will also be 1.  Substitute y = 1  into the equation for the parabola and solve for x:

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:  

**Please see attached diagram for drawn graph. Chord is in red**

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: