how would i find the roots of this parabola - f(x) = 1/3 (x-5)(squared) -8?

Question

need answer soon as possible assignment due on monday

Answer 1

When you are asked to find the roots, it means to find where the function crosses the x-axis. Well, for it to cross the x-axis, that's where ever y is 0, right?

So, plug 0 in for f(x) and solve for x.

0 = (1/3)(x - 5)^2 - 8

Add 8.

8 = (1/3)(x - 5)^2

Divide by 1/3. When you divide by a fraction, you multiply by the reciprocal.

24 = (x - 5)^2

Take root of both sides. But remember, the 24 can be positive OR negative.

+/- root24 = x - 5

+/- 2root6 = x - 5

5 +/- 2root6 = x

So, your roots can be written as: (5 +/- 2root6, 0)

The +/- means plus or minus and is usually written as a plus sign over a minus sign, but this is just easier to write it like this on the computer.

Answer 2

f(x) = 1/3 (x-5)(squared) -8
= 1/3(x^2-10x+25)-8
= x^2/3 -10x/3 +25/3 -8 = 0
x^2-10x +25-24=0
x^2-10x+1 = 0
x = [10 +/- sqrt(100 -4*1*1)]/2
x =[10 +/- sqrt(96)]/2
x = [10 +/- 4sqrt(6)]/2
x = 5 +/- 2sqrt(6)