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:
[tex]x+\frac{1}{4}=0[/tex] and multiply everything by 4:
[tex](4)x+(4)\frac{1}{4}x=(4)0[/tex] and simplify to
4x + 1 = 0 and the factor is
(4x + 1).
Do the same with the 3/2: If
[tex]x=\frac{3}{2}[/tex], then
[tex]x-\frac{3}{2}=0[/tex]. Multiply everything by 2 to get:
[tex](2)x-(2)\frac{3}{2}=(2)0[/tex] to give you
2x - 3 = 0 and the factor is
(2x - 3).
FOIL those 2 factors together to get
[tex]8x^2-12x+2x-3=0[/tex] which simplifies to
[tex]8x^2-10x-3=0[/tex]
Now set it back equal to y and you're done!
