The transformation of the graph from y=x^2 to y=-3(x+5)-2 was analyzed, confirming that the correct interpretation is y=-3(x+5)^2-2. The point (-3, 9) on the original graph transforms to (2, -29) after applying the mapping rule (x, y) → (x+h, ay+k). This transformation involves shifting the x-coordinate by 5 and scaling the y-coordinate by -3, followed by a vertical shift down by 2. The discussion clarifies the importance of correctly interpreting the function notation to ensure accurate transformations.
PREREQUISITESMathematics students, educators, and anyone interested in mastering quadratic transformations and their graphical implications.
Azurin said:Skeeter is assuming the function is [math]y= -3(x+5)^2- 2[/math], not [math]y= -3(x+5) 2[/math].Azurin said:The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2. The point (-3, 9) lies on the graph of y=x^2. Determine its image point after the transformations.
Is that correct?
If so, I would observe that x has 5 added to it and that y (everything done after the squaring) is multiplied by -3 then had 2 subtracted. that is, (x, y) is transformed to (x+ 5, -3y- 2). In particular (-3, 9) is transformed to (-3+ 5, -3(9)- 2)= (2, -29).
Check- yes, if x= 2, [math]y= -3(-2+ 5)^2- 2= -3(3)^2- 2= -27- 2= -29[/math].
The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2.