Which is nRightarrower? f(x)=2x2+3x or g(x)=x2+4

Question

Which is nRightarrower?  f(x)=2x2+3x or g(x)=x2+4

Elaine Verrett · Accepted Answer

Let us write these equations of parabolas in their vertex form i.e.

y = a {(x - h)}^{2} + k

where (h.k) is the vertex and a is quadratic coefficient. The greater the quadratic coefficient, the n\Rightarrower is the parabola.

f (x) = 2 x^{2} + 3 x = 2 (x^{2} + \frac{3}{2} x)

= 2 (x^{2} + 2 \times \frac{3}{4} x + {(\frac{3}{4})}^{2}) - 2 \times {(\frac{3}{4})}^{2}

= 2 {(x + \frac{3}{4})}^{2} - \frac{9}{8}

and

g (x) = x^{2} + 4 = {(x - 0)}^{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) = 2 x^{2} + 3 x

is n\Rightarrower

intacte87 · Accepted Answer

Let&#039;s graph them both and then see for sure. Here is f(x)=2x2+3xAnd this is g(x)=x2+4Why 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 nRightarrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).Let&#039;s compare the graphs of y=±x2,±5x2,±13x2. This is y=x2

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

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