1. Chapter 10: Quadratic Equations & Functions 10.1 Exploring Quadratic Graphs

2. Activity Graph:

3. Standard Form of a Quadratic Function Quadratic function: Quadratic parent function: – The simplest version of a quadratic, y = x 2 Parabola: – The graph of a quadratic function

4. Quadratic Functions Parabolas have symmetry The line that you can fold a parabola on to make two matching halves is called the axis of symmetry Highest or lowest point is called the vertex – if “a” in the equation is < 0, the vertex is a maximum The parabola opens downward – If “a” in the equation is > 0, the vertex is a minimum The parabola opens upward

5. Example 1a Identify the vertex of the graph. Is it a maximum or a minimum?

6. Example 1b Identify the vertex of the graph. Is it a maximum or a minimum?

7. Example 2 Graph:

8. Example 2a Graph:

9. Example 3 Order the quadratics in order of widest graph to narrowest graph:

10. Example 3a Order the quadratics in order of widest graph to narrowest graph:

11. Example 4 How is the graph of y = 2x 2 + 3 different from the graph of y = 2x 2 ?

12. Example 4a How is the graph of y = x 2 - 4 different from the graph of y = x 2 ?

13. Example 5 Suppose you see an eagle flying over a canyon. The eagle is 30 ft above the level of the canyon’s edge when it drops a stick from its claws. The force of gravity causes the stick to fall toward Earth. The function h = -16t 2 + 30 gives the height of the stick h in feet after t seconds. Graph this quadratic function.

14. Example 5a Suppose a squirrel is in a tree 24 ft above the ground. She drops an acorn. The function h = -16t2 + 24 gives the height of the acorn in feet after t seconds. Graph this function.