Write an equation for the parabola shown in the picture.

D. x-2 = (-2/9)(y +3)^2

The parent function, x = y^2 is translated 2 units to the right and 3 units down. This means x is replaced by x-2, and y is replaced by y+3.

There is also a horizontal scale factor involved. It is useful to use the point (0, 0) to determine what it is.

... (x -2) = a(y +3)^2 . . . . . the translated function with unknown factor "a"

... 0 -2 = a(0 +3)^2 . . . . . .substitute (x, y) = (0, 0)

... -2 = 9a . . . . . . . . . . . . . simplify

... a = -2/9 . . . . . . . . . . . . .divide by the coefficient of "a"

So, the graph is described by ...

... (x-2) = (-2/9)(y+3)^2 . . . . . matches selection D

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

hreryryrranswer:

step-by-step explanation: