Question

What are the coordinates of the vertex of the table? Is it a minimum or a maximum?

Answer 1

You can reconstitute the equation of this quadratic function
of te form:y = ax² + bx + c, by giving x and y the various values in the table. For instance: for x = 0, y =1. Plug 0 & 1 in the equation:1 = a(0)² +b(0) + c → c = 1 . You continue with the other values and you will find :
a-b = -3 and
4a - 2b =- 4
Solving it will give y = x² +4x +1
This is a parabola opening upward (because a >0) with an axis of symmetry = -b/2a or x= -2 and a minimum y = (-2)² -2(4)+1 = -3; hence
MINIMUM (-2, -3).
N.B: Your various answers don't mention my result. However in your
C. Answer they are claiming Maximum (-2,-3) and it's wrong it should be MINIMUM.
Please refer to your teacher since I am sure of the result

Answer 2

Answer:

The answer is the option B

$(-2,-3)$ is a minimum

Step-by-step explanation:

using a graphing tool

plot the ordered pairs of the table

Observing the points in the graph the less value of y is equal to $-3$

therefore

the point $(-2,-3)$ is a minimum