The netting of an empty hammock hangs between its supports along a curve that can be modeled by a
parabola. In the illustration shown, the unit of measurement for both axes is feet, and the vertex of the
curve is point C. Find a quadratic function that models the hammock's netting, and state the function's
domain.
8
0
4
2
|(-2.4)
B
(8.4)
C
(3.3)
0
-2
0
2
16
18
10
The equation that models the hammock's netting written as a transformation of the parent function
f)=xis g(x) =
The domain of g(x) is {x|
1.

The function g(x) that models the hammock's netting is [tex]g(x) = \frac{1}{25}(x - 3)^2 + 3[/tex].
The domain of g(x) is [tex]\{-2 \le x \le 8 \}[/tex]

Equation that models the netting

From the graph, we have:

[tex](h,k) = (3,3)[/tex] ---- the vertex

[tex](x_1,y_1) = (-2,4)[/tex] --- point A

[tex](x_2,y_2) = (8,4)[/tex] --- point C

Substitute [tex](h,k) = (3,3)[/tex] in [tex]y = a(x-h)^2 + k[/tex]

[tex]y =a(x - 3)^2 + 3[/tex]

At point A, we have: [tex](x_1,y_1) = (-2,4)[/tex]

So, the equation becomes

[tex]4 = a(-2 - 3)^2 + 3[/tex]

[tex]4 = a(-5)^2 + 3[/tex]

[tex]4 = 25a + 3[/tex]

Collect like terms

[tex]-3 + 4 = 25a[/tex]

[tex]1 =25a[/tex]

Divide both sides by 25

[tex]a = \frac 1{25}[/tex]

Substitute [tex]a = \frac 1{25}[/tex] in [tex]y =a(x - 3)^2 + 3[/tex]

[tex]y = \frac{1}{25}(x - 3)^2 + 3[/tex]

The domain

From the graph, the x value starts at -2 and ends at 8

This means that, the domain of the function is [tex]-2 \le x \le 8[/tex]

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