Question

The table of values represents a quadratic function f(x).

x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23

What is the equation of f(x)?

Answer 1

The equation of the quadratic function is f(x) = (0.5)x^2 + (-4.5)x + 23.

Step-by-step explanation:

The table of values represents a quadratic function. To find the equation of the quadratic function, we need to determine the values of a, b, and c in the quadratic equation of the form ax^2 + bx + c = 0.

Using the given table, we can substitute the x and f(x) values to get three different equations. By solving these equations simultaneously, we can find the values of a, b, and c.

Substituting the values, we find that the equation of the quadratic function is f(x) = (0.5)x^2 + (-4.5)x + 23.