The graph of y = x2 is stretched vertically by a factor of 2 and shifted 5 units left and 2 units down. Write an equation for the new graph.

Question

The graph of y = x2 is stretched vertically by a factor of 2 and shifted 5 units left 

     and 2 units down. Write an equation for the new graph. 

Answer 1

y = 2(x+5)^2 - 2

is y=x^2 stretched vertically by 2, shifted left by 5 and down by 2

general form of the quadratic equation is y=a(x-h)^2 +k where (h,k) is the vertex

stretch vertically means multiply a by the factor of 2

shift left by 5 means replace x by x+5, replace h by h-5, 0 to -5

shift down by 2 means subtract 2, or replace y by y+5, or replace k by k-2, 0 to -2