Which function is equivalent to y=x2-10x+9?

a: y=(x+5)^2+16
b: y=(x-5)^2-16
c: y=(x-5)^2+16
d: y=(x+5)^2-16

B

Step-by-step explanation:

Given

y = x² - 10x + 9

Using the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - 10x

y = x² + 2(- 5)x + (- 5)² - (- 5)² + 9

 = (x - 5)² - 25 + 9

 = (x - 5)² - 16 → B

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.