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.

Accepted Solution

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].