The equation of the quadratic function represented by given table is f(x) = -0.25x² -x + 3.
Given table is:
x y
-3 3.75
-2 4
-1 3.75
0 3
1 1.75
Let us say the quadratic function is:
f(x) = ax² +bx + c
A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are non-zero.
When, x=0, f(x) =3
So, 3 = c
So, f(x) = ax² +bx +3
When, x=1, f(x) =1.75
1.75 = a+b+3
a+b = -1.25........(1)
When, x=-1, f(x) =3.75
3.75 = a-b+3
a-b = 0.75........(2)
Solving equations (1) and (2)
a = -0.25
b = -1
So quadratic function will be:
f(x) = -0.25x² -x + 3
Therefore, the equation of the quadratic function represented by given table is f(x) = -0.25x² -x + 3.
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