The function f(x) is a quadratic function and a limited table of values is provided below. Write the equation of the quadratic polynomial in standard
form.

x^2 - x - 12

Step-by-step explanation:

The quadratic will have the form f(x) = ax^2 + bx + c

Note that when x = 0, y = -12.  Thus, we have f(0) = a(0)^2 + b(0) + c = -12, and the function (so far) is f(x) = ax^2 + bx - 12.

Arbitrarily choose two more ordered pairs from the table.  I've chosen (-3, 0) and (-4, 8).

For (-3, 0), the quadratic becomes 0 = a(-3)^2 + b(-3) - 12, or:

0 = 9a - 3b, and

For (4, 8), f(4) = 8 = a(4)^2 + b(8), or 8 = 16a + 8b, or 1 = 2a + b, or b = 1 - 2a

Solve 0 = 16a + 4b and b = 1 - 2a for a and b.

Let's use substitution:   Substitute b = 1 - 2a into 0 = 9a - 3b or 3a - b = 0:

3a - 1 - 2a = 0, or a = 1.

Since b = 1 - 2a, we get b = 1 - 2(1) = -1

and so a = 1, b = -1 and c = -12

Then the polynomial must be:  x^2 - x - 12

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!