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disa [49]
3 years ago
10

Write an equation for a quadratic function in factored form with

Mathematics
1 answer:
Fittoniya [83]3 years ago
8 0

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 <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:

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

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:

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 <em>x</em> = -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)

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