To graph the expression y = x^2 + kx, we can start by analyzing the equation.

First, let's look at the quadratic term x^2. This term indicates that the graph will be a parabola. Since the coefficient of x^2 is positive (1), the parabola will open upwards.

Next, let's consider the linear term kx. The coefficient of x (k) determines the slope of the line. If k is positive, the line will have a positive slope, and if k is negative, the line will have a negative slope.

To find the vertex of the parabola, we can use the formula x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = 1 and b = k. So the x-coordinate of the vertex is x = -k/2.

Now, let's consider a few different scenarios for different values of k:

1. If k = 0:
In this case, the equation becomes y = x^2, which is a standard upward-opening parabola with the vertex at (0,0). The graph will be symmetrical with respect to the y-axis.

2. If k > 0:
The equation becomes y = x^2 + kx, which means there is an additional positive linear term. This will cause the parabola to shift to the left if k is positive. The vertex will also shift to the left and the graph will be asymmetric.

3. If k < />
The equation becomes y = x^2 + kx, which means there is an additional negative linear term. This will cause the parabola to shift to the right if k is negative. The vertex will also shift to the right and the graph will be asymmetric.

In summary, the graph of the expression y = x^2 + kx will always be a parabola that opens upwards. The position and symmetry of the graph will depend on the value of k.