Question

03.04 LC)

Write the equation of the graph shown below in factored form.

a graph that starts at the top left and continues down through the x axis at negative four to a minimum around y equals negative two point eight and goes up to touch the x axis at negative two and then goes back down to a minimum around y equals negative zero point four and then goes back up to cross the x axis at negative one.

Answer 1

y = (x +4)(x +2)²(x +1)

Explanation:

The function has a generally U shape, so is of even degree. The zero where the graph touches, but does not cross, the x-axis is a zero of even multiplicity. The minimum degree of a function that matches this description is 4. It will have zeros at x=-4, -2 (multiplicity 2), and -1. The constants in the corresponding binomial factors will be the opposite of these values, so the factored form is ...

y = (x +4)(x +2)²(x +1)

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The multiplicity of a zero is the power of the corresponding factor.