Chapter+2.1+Notes

2.1 Quadratic Functions - Polynomial Function - Let n be a nonnegative integer, and let an, an-1… a2, a1, a0, be real numbers with an = 0. The function F( x) = anx^n+ an-1x^n-1 + … + a2x^2 +a1x + a0 Is called a **polynomial function of x with degree n.** The coefficient an is called the **leading coefficient,** and a0 is the constant. - Quadratic Function Let a, b, and c be real numbers with a can’t equal to 0. The function f(x) = ax^2 + bx +c is called a **quadratic equation.** - Graphing Quadratic Functions in Standard Form - Quadratic Function: Standard Form - The quadratic function f(x) = a(x – h)^2 + k is in standard form. The graph of f is a parabola whose vertex is the point (h, k). The parabola is symmetric with respect to the line x = h. If a > 0, the parabola opens up. If a <0, the parabola opens down. - Graphing a Quadratic Function Given in General Form with a Negative Leading Coefficient. - Graph the quadratic function f (x) = -3x^2 + 6x + 2 F (x) = -3x^2 + 6x + 2 = (-3x^2 + 6x) + 2 = -3(x^2- 2x) + 2 = -3(x^2 – 2x +1-1) +2 = -3(x^2 – 2x + 1) – 3(-1) +2 = -3( x – 1)^2 +5