1 Quadratic Functions, Quadratic Expressions, Quadratic Equations Definition: A quadratic function is a function of the formwhere a, b, c are real numbers and a 0.The expression on the right-hand-sideis call a quadratic expression.
2 Quadratic Expressions: Factored Form Examples:1.2.
3 Factoring quadratic expressions: Given where a, b, c are integers.Case 1: a = 1;Since
9 Quadratic Equations:A quadratic equation is an equation of the form:Problem: Find the real numbers x, if any, that satisfy the equation.The numbers that satisfy the equation are called solutions or roots.
10 Methods of Solution:Method 1: Factorthen the solutions (roots) of the equationare
19 Quadratic Functions:The graph of is a parabola. The graph looks likeif a > if a < 0
20 Key features of the graph: The maximum or minimum point on the graph is called the vertex. The x-coordinate of the vertex is:
21 The y-intercept; the y-coordinate of the point where the graph intersects the y-axis. The y-intercept is:The x-intercepts; the x-coordinates of the points, if any, where the graph intersects the x-axis. To find the x-intercepts, solve the quadratic equation
22 Examples:Sketch the graph ofvertex:y-intercept:x-intercepts: