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