Which is narrower?
#f(x)=2x^2+3x# or #g(x)=x^2+4#
2 Answers
f(x)=2x^2+3x# is narrower
Explanation:
Let us write these equations of parabolas in their vertex form i.e.
=
=
and
To find whether a parabola is narrow or wide, we should look at the quadratic coefficient of the parabola, which is
graph{(y-x^2-3x)(y-x^2-4)=0 [-21.08, 18.92, -6, 14]}
Explanation:
Let's graph them both and then see for sure. Here is
graph{2x^2+3x [-10, 10, -5, 20]}
And this is
graph{x^2+4 [-10, 10, -5, 20]}
Why is it that
The answer lies in the coefficient for the
Let's compare the graphs of
graph{(y-x^2)(y+x^2)=0 [-10, 10, -5, 5]}
This is
graph{(y-5x^2)(y+5x^2)=0 [-10, 10, -5, 5]}
And this is
graph{(y-1/3x^2)(y+1/3x^2)=0 [-10, 10, -5, 5]}