Answer:
[tex]y=(x+2)(x-3)[/tex]
Step-by-step explanation:
Given: [tex]y=x^2-x-6[/tex]
To find: a factored form of the given equation
Solution:
The equation [tex]y=ax^2+bx+c[/tex] can be written in factored form as [tex]y=a(x-r_1)(x-r_2)[/tex].
To find the x-intercepts, put [tex]y=0[/tex].
Graph of the equation [tex]y=a(x-r_1)(x-r_2)[/tex] represents a parabola.
[tex]y=x^2-x-6\\=x^2+(-1)x-6\\=x^2+(-3+2)x-6\\=x^2-3x+2x-6\\=x(x-3)+2(x-3)\\=(x+2)(x-3)\\\Rightarrow y=(x+2)(x-3)[/tex]
