H(x)=-5(x-1)^2+45
what is the maximum height

9514 1404 393

  45

Step-by-step explanation:

The equation is that of a parabola in vertex form.

  y = a(x -h)^2 +k

where 'a' is the vertical scale factor and (h, k) is the vertex.

Comparing this to the given function, you find ...

  a = -5

  h = 1

  k = 45

The negative value of 'a' tells you the parabola opens downward, so the y-value of the vertex is the maximum value of the function: 45.

b.-4 units

all you   do is count how many times you move

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt