Answer to Question #147233 in General Chemistry for arjj

Question

Consider a parabola P that is congruent to y 5 x 2 and with vertex (2, 24). Find the equation of a new parabola that results if P is
a) translated 2 units down
b) translated 4 units to the left
c) translated 2 units to the left and translated 3 units up
d) translated 3 units to the right and translate 1 unit down

Answer 1

y = -(x+1)^2 +3

Step-by-step explanation:

Translating f(x) left by 1 unit replaces x with x+1.

Translating f(x) up by 3 units replaces f(x) with f(x)+3.

Reflecting f(x) over the x-axis replaces f(x) with -f(x).

__

When y = x^2 is reflected over the x-axis, it becomes ...

 y = -x^2

When y = -x^2 is translated 1 unit left, it

becomes ...

 y = -(x +1)^2

When y = -(x+1)^2 is translated 3 units up, it becomes ...

 y = -(x +1)^2 +3