Use the provided information to write the standard form equation of the parabola. Opens up or down, and passes through (8,0), (13,-5), and (12,0)

Step-by-step explanation:

Parabola f(x) = ax² + bx + c passing through points (8,0) and (12,0) means that 8 and 12 are its root and (x-8) and (x-12) are its factors

So we get:

               f(x) = a(x - 8)(x - 12)

The parabola passes through point (13, -5) that means if x=13 then f(x)=-5

So:

      -5 = a(13 - 8)(13 - 12)  

      -5 = a(5)(1)

      -5 = 5a

       a = -1          {<0 so parabola opens down}

Therefore:

                 f(x) = -(x - 8)(x - 12)

And expanding:

                f(x) = -(x² - 12x - 8x + 96)

So the standard form equation of the parabola:

                f(x) =  -x² + 20x - 96

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation: