1. 2.1 Quadratic Functions Standard form Applications

2. Quadratic Function Let a, b and c be real numbers with a≠0, then The graph of a quadratic is called a parabola The vertex occurs at the maximum or minimum of the parabola The axis of symmetry is a vertical line through the vertex that splits the parabola in half When a>0 the graph opens up (minimum) When a>0 the graph opens down (maximum)

3. Standard Form of Quadratic Function The vertex is (h, k) The axis of symmetry is the line x = h To write in standard form, find the vertex on your calculator and substitute into the equation Example: Describe the graph and write in standard form

4. Writing an equation from a graph Plug in the vertex for h and k and a point on the curve for x and y Solve for a Write the equation in standard form plugging in a, h and k Example: Write the equation of the graph with a vertex at (1, 2) and passing through the point (3, -6)

5. X-intercepts Where the graph crosses the x-axis The solutions, roots, zeros and x- intercepts are all the same values Use 2 nd TRACE 2:Zero on the calculator to find the x-intercepts If the zero is an integer it will be in the table where y = 0

6. Applications A farmer wishes to fence a rectangular pen for his pigs. He has 36 meters of fence available. What length, x, will result in a pen of maximum area? X

7. Assignment Page 143 # 1-8 all, 23, 25, 35, 37, 41, 45, 53, 63, 67, 69, 73