Two transformations are to be applied to this right triangle in Quadrant II. Which graph shows the triangle together with its final image after a translation 3 units down and 1 unit to the right, followed by a counterclockwise rotation of 90° about the origin?

Remember that for a quadratic function of the form  we can find its vertex with formula:  where  is the x-coordinate of the vertex; then we will find the y-coordinate by replacing  in our original function.

From the question know that  and , so lets replace those values in our vertex formula to find the x-coordinate of our vertex:



Now lets replace that value into our original function to find the y-coordinate of our vertex:



Finally, we have our vertex (6,-9)

Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.