1. The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

2. All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.

3. Sometimes the graphs will contain functions that are non-continuous or discontinuous, meaning that you have to pick up your pencil in the middle of the graph when you are drawing it. Continuous functions means that you never have to pick up your pencil if you were to draw them from left to right.

4. Piecewise functions may or may not be differentiable on their domains. continuous, and we will then see if it is differentiable. Find b and c so that f(x) is differentiable at x = 1 Let's work on continuity first

5. quadratic

6. piecewise

7. , a piecewise-defined function is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain

8. A quadratic function is one of the form f(x) = ax2 + bx + c,