Answer:
[tex]f(x)=-2x(x+4)[/tex]
Step-by-step explanation:
We want to find the equation of a quadratic function in factored form with zeros at x = -4 and x = 0 that passes through the point (-3, 6).
The factored form of a quadratic is given by:
[tex]f(x)=a(x-p)(x-q)[/tex]
Where p and q are the zeros and a is the leading coefficient.
Since we have zeros at x = -4 and x = 0, let p = -4 and q = 0. Substitute:
[tex]f(x)=a(x-(-4))(x-0)[/tex]
Simplify:
[tex]f(x)=ax(x+4)[/tex]
And since we know that the function passes through the point (-3, 6), f(x) = 6 when x = -3. Thus:
[tex](6)=a(-3)(-3+4)[/tex]
Simplify:
[tex]6=a(-3)(1)[/tex]
Thus:
[tex]-3a=6\Rightarrow a=-2[/tex]
So, our quadratic function is:
[tex]f(x)=-2x(x+4)[/tex]
