Question

Write an equation for the parabola shown in the picture.

Answer 1

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

Explanation:

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

Answer 2

D

Explanation:

First, he parabola has a sideways orientation. This signals that x and y have been reversed within the equation meaning
`x^(2) --->y^(2)`. We first look for answers for which y has been raised to the seocnd power instead of x. This leaves answer choice a, b, and d.

Second, we find the vertex of the parabola (center point of the U) at (2,-3). We write them with inverse signs. (x-2) since 2 is the x-coordinate. (y+3) since -3 is the y-coordinate.

The only answer choice meeting these requirements is D.