Answer:
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
