The vertex of a parabola is simply where the function is a maximum or a minimum. In the equation given, we'll look at the right side.
Since the x+3x+3 term is squared, the minimum value of it is 00 (since any squared number is either positive or 00). Thus, when is (x+3)^2=0(x+3)2=0?
(x+3)^2=0(x+3)2=0
x+3=0x+3=0 or -(x+3)=0−(x+3)=0
x = -3 or x = -3x=−3orx=−3
x = -3x=−3
Thus, the vertex is at x=-3x=−3
We can plug this into the original equation to get y=5y=5 so the point of the vertex is (-3,5)(−3,5)
Now, we can plug in other values of xx to get different points on the parabola. Some of which could be:
x=0x=0, so y=1/2y=12 and the point is (0,1/2)(0,12)
x=-1x=−1, so y=3y=3 and the point is (-1,3)(−1,3)
x=-5x=−5, so y=3y=3 and the point is (-5,3)(−5,3)
Then again, you can choose any xx-values and get points on the parabola.