Question #4c04a

1 Answer
Oct 11, 2017

Vertex: (-3,5)(3,5)

Explanation:

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.