Answer and Explanation:
Please note the following:
*When the coefficient of x^2 is positive, the parabola opens upwards and when the coefficient of x^2 is negative, the parabola opens downwards.
*If the parent function is x^2 and we're given a transformation of x^2 + a, it means that the graph of the function will move a-places upwards and if we're given x^2 - a, it means that the graph will move a-places downwards.
*If the parent function is x^2, and we're given (x + a)^2, it means that the graph will move a-places to the left and if we're given (x - a)^2, it means that the graph will move a-places to the right.
Let's go ahead and answer the given question;
* (x - 3 )^2 + 2...........................opens up, shifts 3 units right and 2 units up.
*-(x - 3)^2 - 2............................opens down, shifts 3 units right and 2 units down.
*(x + 3)^2 + 2..........................opens up, shifts 3 units left and 2 units up.
*-(x - 3)^2 + 2.........................opens down, shifts 3 units right and 2 units up.
*(x - 2)^2 + 3...........................opens up, shifts 2 units right and 3 units up.
*(x + 2)^2 + 3..........................opens up, shifts 2 units left and 3 units up.
