MHB Determine its image point after the transformation

[Azurin]

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.

 

[skeeter]

the mapping rule for points on $y=x^2$ to $y=a(x-h)^2+k$ is

$(x,y) \rightarrow (x+h,ay+k)$

reference link ...

Vertex form of a quadratic equation

 

[HOI]

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.

Skeeter is assuming the function is [math]y= -3(x+5)^2- 2[/math], not [math]y= -3(x+5) 2[/math].
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].

 

[HOI]

You wrote

The graph of y=x^2 was transformed to the graph of y=-3(x+5)-2.

Did you mean "y= -3(x+ 5)^2- 2" or just "y= -3(x+ 5)^2"? In other words, did you drop the "^" or did you type "-" instead of "^"?