Answer:
the standard form of the function that models this situation should be [tex]f(x) = -0.5x^{2} +40x[/tex]
Step-by-step explanation:
Lets visualize the table for x and y values first:
0 0
2 78
4 152
6 222
8 288
It is clear from the problem, we have to obtain the values of a, b, and c from the equation f(x) = ax² + bx + c.
We need to make use of data in the table to get the values a, b and c. As a, b, and c are three unknowns, we will have to find three equation using the values in data table.
So, if we put x = 0, and y = 0 in f(x) = ax² + bx + c, we can get the value of c.
f(x) = ax² + bx + c
0 = 0 + 0 + c
Lets put some points or pairs to find the values of a and b.
Putting the pair (6, 222) in f(x) = ax² + bx + c
f(x) = ax² + bx + c
222 = a(6)² + b(6) + 0
222 = 36a + 6b
Dividing the above equation by 6 to further reduce it
37 = 6a + b (Equation 1)
Putting the pair (8, 288) in f(x) = ax² + bx + c
f(x) = ax² + bx + c
288 = a(8)² + b(8) + 0
288 = 64a + 8b
Dividing the above equation by 8 to further reduce it
36 = 8a + b (Equation 2)
Subtracting Equation 2 i.e. 36 = 8a + b from Equation 1 i.e. 37 = 6a + b
1 = -2a
a = -0.5
Putting a = -0.5 in Equation 2
36 = 8a + b
36 = 8(-0.5) + b
36 = -4 + b
b = 40
Hence, the standard form of the function that models this situation should be [tex]f(x) = -0.5x^{2} +40x[/tex]
Keywords: standard form, function
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Answer:
f(x) = -1/2x^2 + 40x + 0
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