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Find a function defined by f(x)=a(x-h)^2+k?
Year x: 51 61 71 81 91 101
Dollars y (in billions): 0.1 0.2 0.6 1.1 2.3 4.7
Find a function defined by f(x)=a(x-h)^2+k that models the data by using (51, 0.1) as the vertex and (101, 4.7) as the second point.
1 Answer
- Wile E.Lv 77 years ago
x = 51
y = 0.1
h = 101
k = 4.7
y = a(x - h)² + k
Subbing known values,
0.1 = a(51 - 101)² + 4.7
0.1 = a(- 50)² + 4.7
0.1 = a(2500) + 4.7
0.1 = 2500a + 4.7
2500a = 0.1 - 4.7
2500a = - 4.6
a = - 4.6 / 2500
a = - 0.0018
Equation:
y = - 0.0018(x - 101)² + 4.7
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Source(s): 3/29/14
