Quadratic Functions and Their Graph Section 11.6 Quadratic Functions and Their Graph

Basic Graph Graph y = f(x) = x²

Complex Quadratic Equation The complex quadratic equation has the form y = f(x) = ± a(x – h)² + k The ±, a, h, and k change the basic graph to create the new complex graph.

Complex Quadratic Equation The complex quadratic equation has the form y = f(x) = ± a(x – h)² + k ± Determines the direction the parabola is facing + graph open upward – graph opens downward

± The difference between the + and -

Complex Quadratic Equation The complex quadratic equation has the form y = f(x) = ± a(x – h)² + k a Determines the width of the graph based on the basic graph y = f(x) = x² 0<a<1 wide graph a>1 narrow graph

a When the a changes the width of the graph changes.

Complex Quadratic Equation The complex quadratic equation has the form y = f(x) = ± a(x – h)² + k h Indicates how much the graph will be moving along the x – axis, the horizontal movement +h moves to the right h units -h moves to the left h units

h What happens when we have a h

Complex Quadratic Equation The complex quadratic equation has the form y = f(x) = ± a(x – h)² + k k Indicates how much the graph will be moving along the y-axis, the vertical movement. +k move up k units -k move down k units

k What happens with a k

Vertex Vertex Lowest point (minimum) or the highest point (maximum) of a graph You will have a lowest point if the sign is + You will have a highest point if the sign is - Algebraically defined by the point (h,k) Find the vertex, then determine if the point is a max or min y = -2(x + 3)² - 1

Graph Example Graph y = -x² - 3

Graph Example Graph f(x) = 2(x + 3)²

Graph Example Graph f(x) = -3(x – 2)² +1

Graph Example Graph y = ½(x - 2)² - 3

Homework Section 11.6 #9, 11, 15, 17,35, 37, 39, 41, 43, 45