If the graph of y = x^2 is rotated 270 degrees counterclockwise about the origin?

Question

If the graph of y = x^2 is rotated 270 degrees counterclockwise about the origin, and then the image is reflected in the line y = x, what is the equation of the resulting graph? Show work to support your answer

Answer 1

Hi,



If the graph of y = x² is rotated 270 degrees counterclockwise about the origin, then the resulting equation is x = y². If x = y² is reflected in the line y = x, then the equation of the resulting graph is y = x², just like the original equation. <==ANSWER



I hope that helps!! :-)

Answer 2

y = x^2 is the answer



the rotation: (y = x^2) is a parabola(bell) about the positive y-axis



rotated 90 is a parabola (same size and shape) about the neg x-axis



rotated 180 is same about the negative y-axis



rotated 270 is same about the positive x-axis



the axial symmetry about the line y=x (the line 45deg tru the origin)



simply moves the 270 rotation back to the y axis where it started

Answer 3

it will look like the x^2 is rotated 90 degrees to the right. Kind of like a y= root x and y= -root x

Answer 4

y=x^2,

the curve is symmetrical about

the +ve y axis thro the origin

rotate 90 deg AC;

the curve is symmetrical about

the -ve x axis thro the origin

rotate by a further 180 deg AC;

the curve is symmetrical about

the +ve x axis thro the origin

reflect in the line y=x;

this is the image of the +ve x

axis,therefore we are back to

where we started



that is,



y=x^2,the vertex being at {0,0},

the curve goes thro the origin

and is symmetrical about the +ve

y axis