Question

Sketch the graph of the function. $$y=x^{2}$$

Short answer

The graph of the function \(y = x^{2}\) is a parabola with its vertex at the origin, (0,0), and opens upward.

Step-by-step solution

Identifying the type of function

The function \(y = x^{2}\) is a basic example of a quadratic function. The general form of a quadratic function is \(y = ax^{2} + bx + c\), but in this case, \(a = 1\), \(b = 0\) and \(c = 0\). The function makes a 'U'-shaped curve called a parabola.

Plot suitable values

Choose a range of x-values (including negative, positive, and zero), and find the corresponding y-values by substituting each x-value into the function. In this case, the chosen x-values could be \(-2,-1,0,1,2\). The corresponding y-values for these x-values would respectively be \(4,1,0,1,4\).

Sketch the graph

Next plot these pairs of values (x,y) on the graph as coordinate points. Joining these points will give a smooth curve of the function \(y = x^{2}\). The parabola has its vertex (its lowest point, because it opens upward) at (0,0).