complete the table for the given function. and EXPLAIN your answer
x y = x2 + (-3)
0
1
2
3
To complete the table, we need to substitute each value of x into the given expression and simplify to find the corresponding value of y.
x y = x^2 - 3
0 0^2 - 3 = -3
1 1^2 - 3 = -2
2 2^2 - 3 = 1
3 3^2 - 3 = 6
So the completed table is:
x | y
------------
0 | -3
1 | -2
2 | 1
3 | 6
The given function is a quadratic function of the form y = ax^2 + bx + c. The coefficient of x is 0 in this function, which means that the graph of the function is a parabola that opens upwards or downwards, but does not shift left or right. The constant term or y-intercept of the function is -3, which means that the parabola intersects the y-axis at the point (0, -3). The vertex, or the highest or lowest point of the parabola, is located at x = -b/2a, which in this case is x = 0, since b = 0. To find the y-coordinate of the vertex, we substitute x = 0 into the function and get y = -3. Therefore, the vertex is located at (0, -3). Knowing these basic features of the graph can help us understand the behavior of the function and make predictions about the values of y for other values of x. For example, we can see that as x increases, y also increases and the parabola opens upwards. We can also see that the minimum value of y is -3, which occurs at x = 0, and that there is no maximum value of y.