Respuesta :
The value of n for the given graph when k(x)=x^2 and p(x)=k(x)+n is negative six (n=-6).
What is the vertex form of parabola?
Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The function given in the problem is,
[tex]k(x)=x^2[/tex]
[tex]p(x)=k(x)+n[/tex]
Put the value of k(x), in the above function,
[tex]p(x)=x^2+n[/tex]
Compare it with the equation of parabola, we get,
[tex]h=0\\k=n[/tex]
Now, in the given graph, the vertex, point are (0,-6). Thus, the value of k is -6.
[tex]k=n=-6[/tex]
Hence, the value of n for the given graph when k(x)=x^2 and p(x)=k(x)+n is negative six (n=-6).
Learn more about the vertex form of the parabola here;
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