1. FURTHER GRAPHING OF QUADRATIC FUNCTIONS Section 11.6

2. Further Graphing of Quadratic Functions Section 11.6 Graph a quadratic equation by plotting points. Identify the vertex of a parabola.

3. Quadratic Functions and Their Graphs Graph by plotting points. XY -2 0 1 2 Section 11.6 XY -2-3 -4 0-3 10 27

4. Quadratic Functions and Their Graphs Graph by plotting points. Quadratic Function  A function that can be written in the form y = ax 2 + bx + c, where a, b, and c are real numbers and a ≠ 0.  The shape of the graph of a quadratic function is called a parabola.  The maximum or minimum value is called the vertex and has ordered pair (h, k).  All parabolas have an axis of symmetry, which is a vertical line running through the vertex, equation x = h. Section 11.6 Vertex (-1, -4) Axis of symmetry x = -1

5. Quadratic Functions and Their Graphs Solve. Quadratic Function  A function that can be written in the form y = ax 2 + bx + c, where a, b, and c are real numbers and a ≠ 0.  Solving the equation equal to zero is the same as saying y=0, or finding the x- intercepts.  Because of symmetry, the x- intercepts will be equidistant from the vertex. Section 11.6 Vertex (-1, -4) Axis of symmetry x = -1

6. Quadratic Functions and Their Graphs Section 11.6 Given an equation of the form y = ax 2 + bx + c, the equation of the axis of symmetry can be found using the formula:  Since the axis of symmetry runs through the vertex, this formula also finds the x-coordinate of the vertex.  To get the y-coordinate, substitute the found x-coordinate back into the quadratic equation.

7. Deriving a Formula for Finding the Vertex Section 11.6 To find the vertex of a parabola in standard form:  Calculate the x-coordinate using the formula  Substitute this value into the original function to calculate the y-coordinate Determine the value of the vertex and graph using the calculator. 1. 2.

8. Quadratic Functions and Their Graphs An object is thrown upward from the top of a 100- foot cliff. Its height in feet above ground after t seconds is given by the function f(t) = -16t 2 +10t +100. Find the maximum height of the object and the number of seconds it took for the object to reach its maximum height.  Minimum/Maximum is the VERTEX  After 5/16ths of a second, the object reaches its maximum height of 101 and 9/16 feet. Section 11.6