Order these Quadratic Functions from the narrowest to widest listed as 1,2,3,4

From narrowest to widest:

1)

2)

3)

4)

Step-by-step explanation:

The "width" of the quadratic function is determined by the value of the coefficient associated by the monomial of highest grade, with respect to the primitive of the quadratic function, represented by , whose ruling coefficient is 1. If the ruling coefficient of the quadratic function is greater than  one, then the curve becomes narrower at the same time that the coefficient increases. Otherwise, if the ruling coefficient of the quadratic function is greater than zero and less than 1, then the curve becomes wider at the same time that the coefficient approximates to zero.

Based on this considerations, we proceed to list the quadratic functions from the narrowest to widest:

1)

2)

3)

4)

Lastly, we include a graphic with all polynomials (tagged as 1, 2, 3, 4) in comparison primitive function (tagged as 0).

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.