Question

Write an equation for a quadratic function in factored form with

Answer 1

Answer:

$f(x)=-2x(x+4)$

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:

$f(x)=a(x-p)(x-q)$

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:

$f(x)=a(x-(-4))(x-0)$

Simplify:

$f(x)=ax(x+4)$

And since we know that the function passes through the point (-3, 6), f(x) = 6 when x = -3. Thus:

$(6)=a(-3)(-3+4)$

Simplify:

$6=a(-3)(1)$

Thus:

$-3a=6\Rightarrow a=-2$

So, our quadratic function is:

$f(x)=-2x(x+4)$