Question

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.

Answer 1

Option B - The parabola is narrower.

Explanation:

Given : The function
`f(x)=x^2` is transformed to
`f(x)=3x^2`

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

Solution :

When the function of parabola
`f(x)=x^2` is transformed by 'a' unit
`f(x)=ax^2`

Then,
`|a|>1` makes the parabola narrow.

and
`0<|a|<1` 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.

Answer 2

Answer: B) The parabola is narrower.

Explanation:

`y=ax^2+bx+c` is the Standard form of a quadratic function, where a, b and c are coefficients (
`a\\eq0`).

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

`|a|>1` makes the parabola narrow.

`0<|a|<1` makes the parabola wide.

Given the transformation of the parent function:
`f(x)=3x^2`, you can identify that:

`a=3`

Then:

`|a|>1`

Therefore, as the parent function is multiplied by 3 and know
`|a|>1`, the parabola if narrower than the parabola of the quadratic parent function
`f(x)=x^2`.