Y-intercept for y=2(x-3)^2+4

The y-intercept for this equation is 22.

Step-by-step explanation:

You can solve this quite easily by assigning a zero value to x and solving for y.  That is where the curve will intersect the x-axis:

y = 2(x - 3)² + 4

y = 2(x² - 6x + 9) + 4

y = 2x² - 12x + 18 + 4

y = 2x² - 12x + 22

EDIT

Note that the expression above is in standard form, though it can also be factored if needed:

y = 2(x² - 6x + 11)

Now we can solve for an x value of zero:

y = 2(0)² - 12(0) + 22

y = 22

So the y-intercept is 22.

40 minutes

step-by-step explanation:

add the time and multiply by 2

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.