Question

Write an equation of a quadratic with roots of -1/4 and 3/2

Answer 1

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:

$x+\frac{1}{4}=0$ and multiply everything by 4:

$(4)x+(4)\frac{1}{4}x=(4)0$ and simplify to

4x + 1 = 0 and the factor is

(4x + 1).

Do the same with the 3/2:  If

$x=\frac{3}{2}$, then

$x-\frac{3}{2}=0$.  Multiply everything by 2 to get:

$(2)x-(2)\frac{3}{2}=(2)0$  to give you

2x - 3 = 0 and the factor is

(2x - 3).

FOIL those 2 factors together to get

$8x^2-12x+2x-3=0$ which simplifies to

$8x^2-10x-3=0$

Now set it back equal to y and you're done!