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Maurinko [17]
3 years ago
9

Which quadratic equation fits the data in the table? x -5,-2,-1,0,3,4,6 y 33,9,5,3,9,15,33

Mathematics
1 answer:
mojhsa [17]3 years ago
6 0

Answer:

y = x² − x + 3

Step-by-step explanation:

Quadratic equation is:

y = ax² + bx + c

Pick three points and plug in.  I'll choose (-2, 9), (-1, 5), and (0, 3).

9 = a(-2)² + b(-2) + c

5 = a(-1)² + b(-1) + c

3 = a(0)² + b(0) + c

9 = 4a − 2b + c

5 = a − b + c

3 = c

We know c = 3, so substitute into the first two equations:

9 = 4a − 2b + 3

5 = a − b + 3

0 = 4a − 2b − 6

0 = a − b − 2

Solve by elimination or substitution.

b = a − 2

0 = 4a − 2(a − 2) − 6

0 = 4a − 2a + 4 − 6

0 = 2a − 2

a = 1

b = -1

Therefore:

y = x² − x + 3

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Next, we'll find the median. The median is the value in the center of the list. Because there are 9 values, that means the center of the list is 5 with four numbers on each side of it. The 5th number in the list is 12, so that's our median.

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