How long does a firework stay in the air?
What is the hang time of a football?
How does a satellite dish work?
Chapter 10 Quadratic Functions Quadratic Functions are used to simulate real-life situations. A quadratic function is an equation in the form: y = ax2 + bx + c
10-1 Graphing Quadratic Functions Objectives: I will be able to graph a quadratic function. I will be able to find the equation of the axis of symmetry and the coordinates of the vertex.
The graph of a quadratic function is called a parabola The graph of a quadratic function is called a parabola. It looks like a U or an upside down U.
Gallileo was the first to show that the path of an object thrown in space is a parabola.
Graphing A Parabola To graph a parabola we create a table of values and then plot the points. Lets Graph: y = x2 – 2x – 3 x y = x2 – 2x – 3 y -2 -1 1 2 3 4
Graphing A Parabola y = x2 – 2x – 3 x y -2 5 -1 -3 1 -4 2 3 4
Graphing A Parabola Lets Graph: y = -x2 + 2x + 1 x y = -x2 + 2x + 1 y -1 1 2 3
Graph It! y = -x2 + 2x +1 x y -1 -2 1 2 3
Parabola Characteristics Quadratic Equation: y = ax2 + bx + c The maximum or minimum point is called the vertex. If a is positive the graph opens up. (Minimum) If a is negative the graph opens down.(Maximum) The line that divides a parabola directly in half is called its axis of symmetry. The axis of symmetry and vertex (turning point) can be found using the equation
The cables that act as suspension are parabolas. Golden Gate Bridge
The general parabola equation is: y = ax2 + bx + c Lets look at the equation: y = -x2 + 4x – 1 a = -1 b = 4 c = -1 Vertex is at y = -x2 + 4x – 1 x y
y = -x2 + 4x – 1 x y -1 1 2 3 4 Vertex? Max or Min? Axis of Symmetry?
The general parabola equation is: y = ax2 + bx + c Lets look at the equation: y = x2 – 2x – 8 a = 1 b = -2 c = - 8 Vertex is at y = x2 – 2x – 8 x y
y = x2 – 2x – 8 x y - 1 - 5 - 8 1 - 9 2 3 Vertex? Max or Min? Axis of Symmetry?
Homework Graphing Parabolas Homework #1