The family of this graph?

Step-by-step explanation:

The shape of this graph is that of a parabola.  In this case the parabola opens down.  The general form of the equation of such a parabola is

y = a(x - h)^2 + k, where (h, k) is the vertex and a is a coefficient to be determined.

In this particular case we can obtain the coordinates of the vertex (h, k) from the graph.  They are (3, 4).  Thus, h = 3 and k = 4.  The graph goes through (1.5, 0).  Use this information to determine the value of the coefficient a:

Then the equation of this parabola must be y = a(x - 3)^2 + 4.

0 = a(1.5 - 3)^2 + 4

Then:

0 = a(-1.5)^2 + 4, or

0 = 2.25a + 4, or

2.25a = -4, or

a = 16/9

Thus, the final result:  The equation of this parabola is

y = (16/9)(x - 3)^2 + 4

whose graph is a parabola that opens down and has vertex (3, 4).            

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d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi