Question

If the parent function f(x) = x2 is vertically stretched by a factor of 2, translated 14 units to the right, then translated 6 units up, write the resulting function g(x) in vertex form

Answer 1

Answer: g(x)=2(x-14)^2+6

Explanation: To shift a parabola to the left or right, you put in the number you want but negative (or the opposite of it) so if in this example you wanted to do 14 you would make it -14. You put this in the parentheses with the x and you square it. To vertically stretch/compress it you put that number in front of the parentheses and the last step is adding on the number you want to shift it up and down. The general equation for this would be f(x)= a(x-b)^2+c. where a= the vertical stretch b= the left and right shift and c= the up and down shift