Answer:
The required equation in factored form is: [tex]\mathbf{y=-4(x+2)(x-1)}[/tex]
Step-by-step explanation:
In this question we need to find the equation of the graph in factored form.
The factored form will be: [tex]f(x)=a(x-r_1)(x-r_2)..[/tex]
where a is y-intercept and r₁, r₂ are x-intercepts
X-intercepts
When y=0, the values of x axis are known as x-intercepts
Y-intercepts
When x=0, the values of y-axis are known as y-intercepts.
Looking at the graph finding x-intercepts
When y=0 x=-2 and 1
So, we have
r₁ = -2
r₂ = 1
Looking at the graph finding y-intercepts
When x=0, y=-4
So, a = -4
Putting values in the formula we will get:
[tex]f(x)=a(x-r_1)(x-r_2)\\f(x)=-4(x-(-2))(x-1)\\f(x)=-4(x+2)(x-1)[/tex]
So, the required equation in factored form is: [tex]\mathbf{y=-4(x+2)(x-1)}[/tex]
