Quadratic Formula Example 1.
f(x)=x²-6x+8.
This particular quadratic equation we could factor it ...
and get the same answer,
but since were in the quadratic formula lesson,
so we're going to use the quadratic formula to solve this.
So, remember the quadratic formula is x=
-b±√(b² - 4ac)
all over 2a.
So, we're going to be plugging in our values.
and simplifying that to get our exact answer and using a ...
calculator to get our decimal answer.
So if I look at this our a value
is here that would be one.
Our b value
-6,
and our c value
is 8.
Plugging that into our quadratic formula we would have x equals
-(-6)
plus or minus the square root
of (-6)² minus 4,
times 1,
times 8,
all divided by
2 times 1.
I'm going go ahead and simplify.
Negative, negative 6 is really positive 6
plus or minus
inside that square root.
-6²  is 36.
4 times 1 times 8 is 32.
So,36 - 32 is would give me 4 inside my radical.
All over 2.
We can take the square root of 4 that would be 2.
And now we just need to split this up and simplify each part.
So we had (6 + 2) over 2.
or (6 - 2) over 2.
6 + 2, would be 8 divided by 2.
6 - 2,
would be 4 over 2.
So, we would end up with 4
or 2,
for our answers.
So then for our exact answers we would have x = 4.
oe
x =2.
Now in this case since we don't have any radicals in our ...
answer, our exact answer and our ...
decimal are actually going to be the same.
We were just rewrite x = 4,
or x = 2.
