Q1 : let f(x)=2x^2−8

the quadratic function g(x) is f(x) translated 2 units down

what is the equation for g(x)

q2 let f(x)=x2−1.

the function g(x) is a vertical stretch of f(x) by a factor of 8.

what is the equation of g(x)?

q3 the graph of the function g(x) is a transformation of the parent function f(x)=x2 .

which equation describes the function g?
(refer to picture attached)
a. g(x)=x2+2
b. g(x)=(x−2)2
c. g(x)=(x+2)2
d. g(x)=x2−2

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

step-by-step explanation: