The quadratic equation that models the data in the table is y = -0.7x^2 + 5.4x + 6
How to determine the quadratic equation?
A quadratic equation is represented as:
y = ax^2 + bx + c
Using the values in the table, we have:
c = 6
a + b + c = 10.7
4a + 2b + c = 14
Substitute c = 6 in a + b + c = 10.7 and 4a + 2b + c = 14
a + b + 6 = 10.7
4a + 2b + 6 = 14
This gives
a + b = 4.7
4a + 2b = 8
Multiply a + b = 4.7 by 2
2a + 2b = 9.4
Subtract 2a + 2b = 9.4 from 4a + 2b = 8
4a - 2a + 2b - 2b = 8 - 9.4
Evaluate
2a = -1.4
Divide by 2
a = -0.7
Substitute a = -0.7 in a + b = 4.7
-0.7 + b = 4.7
Evaluate
b = 5.4
So, we have:
y = -0.7x^2 + 5.4x + 6
Hence, the quadratic equation that models the data in the table is y = -0.7x^2 + 5.4x + 6
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