Given y-k=a(x-h)^2, a=-1, h> 0, k< 0 in which quadrant is the vertex

Since the equation is a quadractic, the graph would be a parabola.

With a being -1, the parabola will represent a reflection of the y values. In other words, the parabola will be upside down and the vertex will be a maximum value. Ultimately, the a in the function doesn't determine the location of the vertex.

Since the k value is negative, that means the equation begins y - (-k). The K value being negative restricts the transformation of the parabola to being down k number of units. The location of moving the parabola down places the vertex in the third or fourth quadrant.

The h value being positive means that the parabola is shifted to the right h number of units. For example, if the parabola f(x) = x²  has a vertex at (0,0), the parabola f(x) = (x-2)² must have a vertex at (2,0) because 2 - 2 = 0. Shifting right places the vertex of the parabola in the first or fourth quadrant.

Therefore the k value and h value restrictions must overlap in the fourth quadrant.

Step-by-step explanation:

d is correct

step-by-step explanation:

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.