At what point is the vertex? Is it a minimum or maximum?
(-2,7);maximum
(-1,0);minimum
(2,-9);minimum
(0,-5);minimum
(2,-9);maximum
(4,-5);maximum

(2, -9); minimum

Step-by-step explanation:

The vertex is the point that either has the largest y value (maximum) or it has the smallest y value (minimum). It is also the point on the graph where if it's a maximum, all the points to the left and right of it are less than it and if it's a minimum, all the points to the left and right of it are more than it.

Looking at the table, we see that the smallest y value is -9. The values beside it are -5 and -8, where are both greater than -9. So, this is a very potential candidate for minimum.

The largest y value is 7. We can't see all the values beside it, but we can guess from the trend, that the y values on one side will be more. So, it can't be a maximum.

Thus, the vertex is at the minimum (2, -9).

Hope this helps!

(2,-9);minimum

Step-by-step explanation:

Since the data is symmetrical about x = 2,

Vertex is (2, -9)

On both sides of x = 2, the y values are greater than -9. Therefore it's a minimum point

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.