when looking at graphs that represent functions of the form y=ax^2, how can you tell which graph will have the largesr value for a, if a is a positive number?

Question

anonymous · Answer

$$y=ax ^{2}$$ is the equation of a parabola along Y axis, right?

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Bad drawing, but,

Let’s take a look at the first form of the parabola.
 $$f(x) = a(x-h)^{2} + k$$

There are two pieces of information about the parabola that we can instantly get from this function.  First, if a is positive then the parabola will open up and if a is negative then the parabola will open down.  Secondly, the vertex of the parabola is the point (h,k).
or in this instance, the origin (0,0)

anonymous · Answer

If you plot the graphs of $$y=x^2 , y= 2x^2 and y=6x^2 $$
you will notice that as the a value increases, the graph kinda gets narrower.