A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The correct option is graph B.
What is the Equation of a parabola?
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given that the function f(x)=x², which represents a parabola, therefore, the function of g(x) can be represented as,
[tex]g(x)=\dfrac13 f(x)\\\\g(x)=\dfrac13 x^2[/tex]
Now, if we compare the function g(x) with the general equation of a parabola, therefore, the value of 'a' will be 1/3 which means that the function will open wider than f(x).
Thus, the correct option is graph B.
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