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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.

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luisejr77

Answer:  B) The parabola is narrower.

Step-by-step explanation:

[tex]y=ax^2+bx+c[/tex] is the Standard form of a quadratic function, where a, b and c are coefficients ([tex]a\neq0[/tex]).

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

[tex]|a|>1[/tex] makes the parabola narrow.

[tex]0<|a|<1[/tex] makes the parabola wide.

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

[tex]a=3[/tex]

Then:

[tex]|a|>1[/tex]

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

Answer:

Option B - The parabola is narrower.

Step-by-step explanation:

Given : The function [tex]f(x)=x^2[/tex] is transformed to  [tex]f(x)=3x^2[/tex]

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

Solution :

When the function of parabola [tex]f(x)=x^2[/tex] is transformed by 'a' unit [tex]f(x)=ax^2[/tex]

Then, [tex]|a|>1[/tex] makes the parabola narrow.

and [tex]0<|a|<1[/tex] 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.

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