Any quadratic function whose leading coefficient is greater than 1 is narrower than [tex]h(x) = x^2[/tex].
The function [tex]h(x) = x^2[/tex] belongs to the family [tex]y = a\cdot x^{2}[/tex], where [tex]a[/tex] is a real coefficient. The greater the [tex]a[/tex], the narrower the graph. Hence, any function whose leading coefficient is greater than [tex]a[/tex] presents a narrower form, that is, [tex]y[/tex] shows greater values for a given value of [tex]x[/tex].
Any quadratic function whose leading coefficient is greater than 1 is narrower than [tex]h(x) = x^2[/tex]. [tex]\blacksquare[/tex]
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