How do you find the equation of a parabola in standard form with x intercepts at -2 and 6 passing through 1 and 8?

Since we know the intercepts, its best to solve the general form first and then convert to the standard form.

The intercepts tell us that for some constant, a

y=a*(x+2)(x-6)

We also know that the parabola must run through a given point (1,8) so we can plug that value in to get our value of a

8=a*(3)(-5)

a=-8/15

Next, expand the formula and start moving numbers around until you are in standard form

y=-8/15*(x²-4x-12)

y=-8/15*((x-2)²-16)

y=-8/15*(x-2)²+128/15