Identify the parent function of the equation below.

y = x² ⇒ answer C

Step-by-step explanation:

* Lets explain the problem

∵ The function is y = 1/2 x² + 3 , that means the parent function is

  transformed by some transformation

- If the parent function is y = x²

- y = x² is a quadratic function represented graphically by upward

 parabola with vertex (0 , 0)

∵ y = x² changed to y = 1/2 x² that means we multiply each

  y-coordinates of the points on the graph of the function by 1/2

∴ The graph of the function is  compressed vertically by scale

   factor 1/2

- That means the graph is squeezing toward the x-axis

∵ y = 1/2 x² changed to y = 1/2 x² + 3 that means we add each

  y-coordinates of the points on the graph of the function by 3

∴ The function translated 3 units up

- That means the vertex of the parabola changed to (0 , 3)

∴ The new function is y = 1/2 x² + 3

* The parent function of y = 1/2 x² + 3 is y = x²

# Look to the attached graph for more understand

- y = x² ⇒ the red graph (parent function)

- y = 1/2 x² + 3 ⇒ the blue graph

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !