The function of the table is quadratic in nature and is given as follows: y = 2x² -1
<h3>What is a quadratic function?</h3>
A quadratic function is one of the following: f(x) = ax² + bx + c, where a, b, and c are positive integers and a, b, and are not equal to zero.
Given the nature of a quadratic function (y = ax² + bx + c) we pick three pairs of (x, y) from the table as follows:
A) (0, -1)
B) (1, 1)
C) (2, 7)
Then we say:
A) (0, -1) → -1 = a(0)² + b(0) + c =
-1 = c ..................................1
B) (1, 1) → 1 = a(1)² + b(1) + c =
1 = a + b + c.......................2
C) (2, 7) → 7 = a(2)² + b(2) + c
7 = a (4) + 2b + c
7 = 4a + 2b + c .................3
Using elimination and substitution, let us substitute equation 1 into equation 2;
that is
1 = a + b + (-1)
1 = a + b -1
1 + 1 = a + b
2 = a + b................................4
From the above we can also say,
b = 2 - a...................................5
substitute 5 into 3 we have
7 = 4a + 2 (2-a) + (-1)
7 = 4a + 4 - 2a - 1
7 = 4a - 2a + 4 - 1
7 = 2a + 3
7- 3 = 2a
4 = 2a
a = 4/2
a = 2
taking [a = 2] and [c = -1], subsitute these into equation 2
1 = a + b + c
1 = 2 + b + (-1)
1 = 2 + b - 1
1 = 2 - 1 + b
1 = 1 + b
b = 1-1
b= 0
Hence,
a = 2
b = 0
c = -1
Hence:
y = 2 * x² + (0) x + (-1)
y = 2x² -1
Hence the equation for the above table is y = 2x² -1
Learn more about Quadratic Functions:
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