Clearly label your answers as A, B, and C.
Given the parent function y=x^2 write the equations with the following transformations in the form y=a(x−h)^2 +k.
A. The graph has been shifted to the right 2 and down 3.
B. The graph has been reflected over the x-axis and stretched vertically by a factor of 2.
C. The graph has been compressed vertically by a factor of 1/3 and shifted left 5.
A. y = x^2 - 4x + 1
B. y = -2x^2
C. y = (1/3)(x + 5)^2
are you sure
I apologize for the error in my response. Let me correct that:
A. y = (x - 2)^2 - 3
B. y = -2x^2
C. y = (1/3)(x + 5)^2
can you explain each part correctly
Certainly! Here's the correct explanation for each part:
A. The transformation (x-2) represents a shift of the graph to the right by 2 units, and the "-3" represents a shift of the graph down by 3 units. Therefore, the equation (x-2)^2 - 3 represents the parent function y=x^2 shifted 2 units to the right and 3 units down.
B. The transformation "-2" represents a reflection over the x-axis, which means the graph is flipped upside down, and the "2" before x^2 represents a vertical stretch by a factor of 2. Therefore, the equation -2x^2 represents the reflection over the x-axis and a vertical stretch by a factor of 2 of the parent function y=x^2.
C. The transformation (1/3) signifies a vertical compression by a factor of 1/3, making the graph shorter and wider, and the transformation (x+5) represents a shift of the graph to the left by 5 units. Therefore, the equation (1/3)(x + 5)^2 represents the parent function y=x^2 compressed vertically by a factor of 1/3 and shifted 5 units to the left.