Answer:
The factored form of a quadratic equation is
[tex]y=a(x-m)(x-n)[/tex]
Where [tex]m[/tex] and [tex]n[/tex] are real numbers.
Though this form, we can deduct the parabola direction, if it opens upside or downside. Additionally, we can also deduct the x-axis interceptions, which in this case are [tex]x=m[/tex] and [tex]x=n[/tex], they are also called the roots of the equation.
The vertex form of a quadratic equation is
[tex]y=a(x-h)^{2} +k[/tex]
Using this form we can deduct the parabola direction, if opens up or down. Also, we can deduct the vertex of the parabola, which has coordinates [tex](h,k)[/tex], parameters of the vertex form.
Therefore, as you can observe, the different forms of a quadratic equation can give us different information.
