Answer:
The graph shifts 3 units left and 15 down. It narrows by a factor of 2 and is right side up.
Explanation:
There are two ways of doing this. You can graph it, or you can put it in the vertex form by completing the square.
A quick way of putting this into the vertex form is write the general equation
y = a(x - h)^2 + k
h= - b/2a = - 12/4 = - 3
- So far what you have is
- y = 2(x - - 3)^2 + k
- y = 2(x + 3)^2 + k
- k = f(x) = f(-3) = 2*(-3)^2 + 12(-3) + 3
- k = 2(9) - 36 + 3
- k = - 18 + 3 = - 15
So the equation in vertex form is
y = 2(x + 3)^2 - 15
Description
y = 2(x + 3)^2 - 15
shifts 3 units to the left and 15 units down. It also narrows by a factor of 2. Finally, it is right side up.
Graph
Since you have seen the graph before, there is not much more to add. It just shows what has been written above.