a To complete the table, we must substitute each value of x in the function and simplify the right-hand side to find its corresponding y-value.
|c|c|c|
[-1em]
x & x^2 & y [0.3em]
[-0.8em]
- 4 & ( - 4)^2 & 16 [0.5em]
[-0.8em]
- 3 & ( - 3)^2 & 9 [0.5em]
[-0.8em]
- 2 & ( - 2)^2 & 4 [0.5em]
[-0.8em]
- 1 & ( - 1)^2 & 1 [0.5em]
[-0.8em]
0 & 0^2 & 0 [0.5em]
[-0.8em]
1 & 1^2 & 1 [0.5em]
[-0.8em]
2 & 2^2 & 4 [0.5em]
[-0.8em]
3 & 3^2 & 9 [0.5em]
[-0.8em]
4 & 4^2 & 16 [0.5em]
We can plot these ordered pairs in a coordinate plane. Then we will connect them with a smooth curve.
b Looking at the graph we made in Part A, we see that the parabola is opening upwards and has a minimum at (0,0). Since the vertex is a minimum or maximum of the parabola, point (0,0) is a vertex.
