How do I get this graph and how do I get it with multiplicity polynomials​

The x-intercept

x

=

−

3

is the solution to the equation

(

x

+

3

)

=

0

. The graph passes directly through the x-intercept at

x

=

−

3

. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.

The x-intercept

x

=

2

is the repeated solution to the equation

(

x

−

2

)

2

=

0

. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.

(

x

−

2

)

2

=

(

x

−

2

)

(

x

−

2

)

The factor is repeated, that is, the factor

(

x

−

2

)

appears twice. The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor,

x

=

2

, has multiplicity 2 because the factor

(

x

−

2

)

occurs twice.

Step-by-step explanation:

answer: a

step-by-step explanation: the answer is a due to the rule of symmetry; that a line of symmetry must divide a figure into 2 pieces that are the exact same, only reflected over a line of symmetry. b and c do not have lines of symmetry and would not divide the figure evenly, thus making the answer a.