Functions and Trig Midterm Exam

A quadratic function is a polynomial function of degree 2, typically in the form of $$f(x) = ax^2 + bx + c$$ where a, b, and c are constants and @@a eq 0@@.

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

The standard form of a quadratic equation is $$y = ax^2 + bx + c$$ .

The axis of symmetry can be found using the formula $$x = -\frac{b}{2a}$$ .

The 'a' value determines the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a < 0$$ , it opens downwards.

The end behavior describes how the function behaves as $$x$$ approaches positive or negative infinity.

The slope of a line is a measure of its steepness, calculated as the change in y over the change in x (rise over run).

An undefined slope occurs in vertical lines where the change in x is zero, leading to division by zero.

The general form of a linear equation is $$Ax + By + C = 0$$ where A, B, and C are constants.

A function is increasing if its derivative is positive and decreasing if its derivative is negative.