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.

Equation of a parabola

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.

Given to us

k(x) = x^2

p(x) = k(x) + n

Substitutionsubstituting the value of k(x) in p(x).

p(x) = k(x)+n

p(x) = x² + n

Comparing

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.

Coordinates 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:

If the function f(x) is translated k units up, then its image is g(x) = f(x) + kIf the function f(x) is translated k units down, then its image is g(x) = f(x) - kThe vertex form of the quadratic function is f(x) = a(x - h)² + k, where a is the coefficient of x² and (h, k) is the vertex

∵ 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)

Turkey temperature = 185 F

Room temperature = 70 F

after 30 minutes if turkey's temperature  = 150 F

so    150  = 185 - K( 185 -70) 30

      K =  ( 185- 150)  /   30 (115)

       K =   35   /  3450

       K=    7  /  690

T(45)  =   185 - (45) ( 7 / 690) (115)

          185 - 52.5   =  132.5

  Temperature after 45 minutes =   132.5 F