Answer:
[tex]\large\boxed{y=(x+2)(x-2)}[/tex]
Step-by-step explanation:
Factored form of quadratic equation:
[tex]y=a(x-x_1)(x-x_2)[/tex]
x₁, x₂ - zeros
We have zeros: x₁ = -2 and x₂ = 2. Substitute:
[tex]y=a(x-(-2))(x-2)=a(x+2)(x-2)[/tex]
We have the vertex (0, -4). Put the coordinates of the vertex to the equation:
[tex]-4=a(0+2)(0-2)[/tex]
[tex]-4=a(2)(-2)[/tex]
[tex]-4=-4a[/tex] divdie both sides by (-4)
[tex]1=a\to a=1[/tex]
Finally:
[tex]y=1(x+2)(x-2)=(x+2)(x-2)[/tex]
