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Identify the parent function of the equation below.

Identify the parent function of the equation below.-example-1

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3 votes

Answer:

y = x² ⇒ answer C

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

Identify the parent function of the equation below.-example-1
User Vith
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