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Answer:
Step-by-step explanation:
First and foremost, a root is the same thing as a zero. It's called a zero because when x is equal to -1/4 (as it is here), y = 0. Where y = 0 is the x-axis. So if a quadratic has a 0 of -1/4, that is where the graph of the parabola goes through the x-axis.
If your quadratic has a zero of -1/4, that means that when y = 0, x = -1/4. Again, because this is a zero of the quadratic, then we can write it in factor form by setting x = -1/4 equal to 0. Do that like this:
If x = -1/4, then x + 1/4 = 0 and the factor is (x + 1/4) However, we do not want to leave that as a fraction. Take care of the fraction when it is set to equal 0:
and multiply everything by 4:
and simplify to
4x + 1 = 0 and the factor is
(4x + 1).
Do the same with the 3/2: If
, then
. Multiply everything by 2 to get:
to give you
2x - 3 = 0 and the factor is
(2x - 3).
FOIL those 2 factors together to get
which simplifies to
Now set it back equal to y and you're done!