# MPM2D1-02 Applying factoring: finding roots of quadratics 2016-12-01

We applied our factoring skills to convert quadratic equations in Standard Form ($y=ax^2+bx+c$) to Factored Form ($y=a(x-r)(x-s)$). It’s the same process as we’ve been using for factoring expressions, but there’s an extra step at the end to factor out any coefficients on the linear terms. For example, if you factor an equation and get to this point:

$y=2(3x-1)(5x+2)$

you can then factor out 3 and 5 from the binomial factors:

$y=(2)(3)(5)(x-\frac{1}{3})(x+\frac{2}{5})$

$y=30(x-\frac{1}{3})(x+\frac{2}{5})$

This is in factored form, and you can read the roots: $(\frac{1}{3},0)$ and $(-\frac{2}{5},0)$.

For class/homework, convert these equations to Factored Form:

$y = \frac{3}{2}x^2-\frac{11}{4}x-\frac{7}{4}$

$y = -14x^2-49x+343$

Enjoy!