Which of the quadratic functions has the narrowest graph? y= -2x^2, y= 1/2x^2, y= 1/7x^2, y= -4x^2

Accepted Solution

Answer: y = -4x^2.


The coefficient of the quadratic term tells you how much the graph of the given function is  stretched vertically (widen horizontally) compared with the parent function (in this case f(x) = x^2).

These are the cases. Given y = Ax^2, for A ≠ 0,

- if |A| > 1, the function is stretched vertically; this is the graph of Ax^2 is narrower than the graph of the parent function, x^2.

- if |A| < 1, the function is stretched horizontally, this is the graph is wider than the graph of x^2.

The greater |A| the narrower the graph.

That is because for the same x-value, f(x) is further of the y-axis as |A| is greater.

So, you conclude that the function f(x) = - 4x^2 is the narrowest function (it is strectched the most) among the choices.

Of course, you can see it if you draw the graphs of the 4 functions in the same coordinate system.