Final answer:
A quadratic relation of the form y=ax²+bx+c, where a is not zero, does not have a linear graph. It will have both a y-intercept and an axis of symmetry, as well as a single vertex.
Step-by-step explanation:
The student asked about a quadratic relation of the form y=ax²+bx+c, where a≠0 (meaning 'a' is not zero), and which characteristic it does not have. A quadratic equation of this form will always have a y-intercept, which you can find by setting x to 0 and solving for y, giving you the point (0, c). The graph of a quadratic equation is a parabola, not a linear graph, so it will not be a straight line. A quadratic function also has an axis of symmetry, which lies along the vertical line x = -b/(2a), and a vertex, which is the highest or lowest point on the graph, depending on the direction the parabola opens.