The function f(x) = x2 is transformed to f(x) = 3x2. which statement describes the effect(s) of the transformation on the graph of the original function?
a)the parabola is wider.
b)the parabola is narrower.
c)the parabola is wider and shifts 3 units up.
d)the parabola is narrower and shifts 3 units down.

 B) The parabola is narrower.

Step-by-step explanation:

is the Standard form of a quadratic function, where a, b and c are coefficients ().

With the coefiicient "a" you can determine how narrow or wide the parabola is:

makes the parabola narrow.

makes the parabola wide.

Given the transformation of the parent function: , you can identify that:

Then:

Therefore, as the parent function is multiplied by 3 and know ,   the parabola if narrower than the parabola of the quadratic parent function .

Option B - The parabola is narrower.

Step-by-step explanation:

Given : The function is transformed to  

To find : Which statement describes the effect(s) of the transformation on the graph of the original function?

Solution :

When the function of parabola is transformed by 'a' unit

Then, makes the parabola narrow.

and makes the parabola wide.

On comparing with given function,

|a|=|3| >1 which is greater than 1.

Which means it makes the parabola narrow.

Therefore, the parabola is narrower.

So, Option B is correct.

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

m a t h w a y. c o m

step-by-step explanation: