Question

Write an equation for a quadratic function in factored form with

zeros at x = -4 and x = 0 that passes through the point (-3,6).

Answer 1

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

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)`