Describe the translation. y=(x+3)2+4 y = ( x + 3 ) 2 + 4 → y=(x+1)2+6

Answer 1

The easiest way to put it is that the constant (the number by itself) inside the parentheses denotes horizontal movement opposite of the sign. The constant outside the parentheses denotes vertical movement.

The parent function is y = x². If we want to move it left 3, we get y = (x + 3)² and if we want to also move it up 4, we get your original function, y = (x + 3)² + 4

So, what if we go from y = (x + 3)² + 4 to y = (x + 1)² + 6

Well, 1 is 2 less than 3, but since movement is opposite, we are moving 2 to the right. Six is 2 more than 4, so we are moving 2 up.

Translation 2 units right and 2 units up.

Answer 2

The translation is from y = (x+3) *2 + 4 to y (x+1) 2 + 6.

The constants in the parenthesis are the negative horizontal movement from the original equation of y = x * 2 and the last constant is the vertical movement.

The +3 in the first equation is a -3 movement from the original equation of y = x * 2.

The + 1 in the second equation is a -1 movement from the original. Thus the movement from the first to the second is + 2 or 2 units to the right.

The first equation is 4 units up from the original equation of y = x * 2

The second equation is 6 units up from the original equation. Thus the movement from the first to second is 2 units up.