To compare the function [tex]\( y = 0.3x^2 \)[/tex] to the parent function [tex]\( y = x^2 \)[/tex], let us analyze their graphical characteristics and how the coefficient affects the shape of the parabola. The parent function [tex]\( y = x^2 \)[/tex] has a coefficient of 1 for [tex]\( x^2 \)[/tex]. This coefficient affects the "width" or "narrowness" of the parabola.
The general form of a quadratic function is [tex]\( y = ax^2 \)[/tex], where [tex]\( a \)[/tex] is a coefficient that determines the shape of the parabola:
1. When [tex]\( |a| > 1 \)[/tex], the parabola becomes narrower than the parent function [tex]\( y = x^2 \)[/tex]. This is because the larger coefficient causes the function to grow more quickly, pulling the sides of the parabola closer together.
2. When [tex]\( |a| < 1 \)[/tex], the parabola becomes wider than the parent function [tex]\( y = x^2 \)[/tex]. In this case, the smaller coefficient means the function grows more slowly, causing the sides of the parabola to spread out more.
For the given function [tex]\( y = 0.3x^2 \)[/tex], the coefficient [tex]\( a \)[/tex] is 0.3. Since [tex]\( 0.3 < 1 \)[/tex], it falls into the second category where [tex]\( |0.3| < 1 \)[/tex].
Therefore, since the coefficient 0.3 is less than 1, the parabola described by the function [tex]\( y = 0.3x^2 \)[/tex] is wider compared to the parent function [tex]\( y = x^2 \)[/tex].
Thus, the function [tex]\( y = 0.3 x^2 \)[/tex] is Wider than the parent function [tex]\( y = x^2 \)[/tex].
