calculus and algebra

Question

Find the equation of the curve which is the image of the parabola y=2x²-x Oxy Cartesian coordinate system with respect the parallel translation defined by the vector P( 3; 5)

Answer 1

This is translations, which is back from precalculus. We want to move the equation to the right 3, and up 5. So x=>x-3 y=>y-5

y-5=2(x-3)^2-x=2(x^2-6x+9)-(x-3)=2x^2 -12x+18-x+3= 2x^2 -13x+21

or

y=2x^2-13x+26

That is your translated equation.