In order to get a grasp on quadratic relations, it is important to develop a thorough understanding of the parabola terminology.
Vertex. The vertex is the turning point of the parabola – essentially the “tip” of the curve. The vertex would be the bottom point of a parabola that opens upward and the top point of a parabola that opens downward.
Optimum Value. Think of this as a fancy term for the y-value of the vertex. The optimum value would be the “minimum” y-value for a parabola that opens upward, and the optimum value would be the “maximum” y-value for a parabola that opens downward.
*Optimization is finding the maximum or minimum value of a certain variable (the variable is the y-value in this case)
Zero(s). When people refer to the “zero(s)” of a parabola, they’re referring to its x-intercept(s). You can identify the zero(s) by finding the x-value(s) for which the y-value is 0.
Axis of Symmetry. A line of symmetry that divides the parabola in half, passing through the vertex. The Axis of Symmetry (or, as I like to call it, the AOS) is equidistant from the two zeros.
*If a parabola only has one zero, then the zero would also be the vertex and the AOS would simply pass through that point.