If k(x) = x^2 and p(x) = k(x) + n, what is the value of n? Pleaseee help ASAP!

I will give brainliest :)

The value of the n is -6.

y = a(x-h)2 + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

k(x) = x^2

p(x) = k(x) + n

p(x) = k(x)+n

p(x) = x² + n

Comparing with the Equation of a parabola,

y = a(x-h)2 + k

p(x) = x² + n

Therefore, the value of n is k which is the y coordinate of the vertex of the parabola.

Looking at the coordinates of the vertex of the parabola,

(h, n) = (0, -6)

Hence, the value of the n is -6.

Learn more about Parabola:

link

The value of n is -6

Step-by-step explanation:

∵ k(x) = x²

→ Its graph is a parabola with vertex (0, 0)

∴ The vertex of the prabola which represents it is (0, 0)

∵ The given graph is the graph of p(x)

∵ Its vertex is (0, -6)

∴ h = 0 and k = -6

∵ a = 1

→ Substitute them in the form above

∴ p(x) = 1(x - 0)² + -6

∴ p(x) = x² - 6

→ Substitute x² by k(x)

∴ p(x) = k(x) - 6

∵ p(x) = k(x) + n

→ By comparing the two right sides

∴ n = -6

∴ The value of n is -6

Look at the attached figure for more understanding

The red parabola represents k(x)

The blue parabola represents p(x)

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80

step-by-step explanation: