Question

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Answer 1

Answer:

p(x)=a$x^{2}$+6ax+5a, where 'a' is a constant

Step-by-step explanation:

Since the graph has only a single curve, it will have two roots, thus it is a quadratic function.

Let the quadratic function be p(x)=a$x^{2}$+bx+c

This can also be written as y=a$x^{2}$+bx+c

from the graph, we see that p(x)=0 when x=(-1),(-5)

therefore, (-1) and (-5) are the roots of the equation.

The relation between the roots of a quadratic function and the coefficients of the quadratic function is

sum of roots=-b/a => -1 + (-5)=-b/a => b=6a

product of roots=c/a => (-1)*(-5)=c/a => c=5a

Thus the quadratic function can be written as p(x)=a$x^{2}$+6ax+5a, where 'a' is a constant

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Answer 2

Answer:

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