Which is n\Rightarrower? f(x)=2x^2+3x or g(x)=x^2+4



Answered question


Which is n\Rightarrower?
f(x)=2x2+3x or g(x)=x2+4

Answer & Explanation

Elaine Verrett

Elaine Verrett

Beginner2021-12-16Added 41 answers

Let us write these equations of parabolas in their vertex form i.e.
y=a(xh)2+k where (h.k) is the vertex and a is quadratic coefficient. The greater the quadratic coefficient, the n\Rightarrower is the parabola.
and g(x)=x2+4=(x0)2+4
To find whether a parabola is n\Rightarrow or wide, we should look at the quadratic coefficient of the parabola, which is 2 in f(x) and 1 in g(x) and hence f(x)=2x2+3x is n\Rightarrower


Beginner2021-12-17Added 42 answers

Let's graph them both and then see for sure. Here is f(x)=2x2+3x
And this is g(x)=x2+4
Why is it that g(x) is fatter than f(x)?
The answer lies in the coefficient for the x2 term. When the absolute value of the coefficient gets bigger, the graph gets n\Rightarrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).
Let's compare the graphs of y=±x2,±5x2,±13x2. This is y=x2

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