SOLUTION: Hi tutor ! So im a 14 year old who lives in texas . Ive really been struggling with the quadratic formula and would love for you to help me where i need help . Please please please

Question 962773: Hi tutor ! So im a 14 year old who lives in texas . Ive really been struggling with the quadratic formula and would love for you to help me where i need help . Please please please respond here , on my email , or through text 2144317404 ! Thank you and God bless you .
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The quadratic formula is about a "general"
quadratic equation, namely:

Then you set to find the "roots"'
which are the solutions

------------------------
Suppose your equation for finding roots looks like:

Then, comparing to the "general" equation:

----------------
Now you have to plug these values into the "general"
formula for finding the roots:

The tricky thing about this formula is that it is TWO formulas:

and

-------------------------------------
That's because of the + or - in front of the square root sign
---------------------------
Now plug in values:

That is one complex solution
The other one is:

---------------------------------
So, you ended up with what they call a pair of
complex conjugate roots. That just means they
look like:
and
-----------------------------
Then there is the whole discussion of the "discriminant"
which is the part of the formula
Because this is under the square root sign, the
"discriminant" will tell you whether you have:
(1) one "double" root in the case where:

(2) two rational roots when:

(3) that pair of complex conjugate roots where:

--------------------------------
The picture of the quadratic ( parabola ) tells you right
away which case you have:
(1) the parabola just touches the x-axis
(2) the parabola crosses the x-axis in 2 places
(3) the parabola never touches the x-axis
---------------------------------------
Here's a plot of the 3 cases of the discriminant:

Hope this helps

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