1. Warm-Up Find a linear function that describes the situation, and solve the problem. 4 minutes 1) A tractor rents for $50, plus $5 per engine hour. How much does it cost to rent and run the tractor for 6 hours?

2. 12.4 Quadratic Functions 12.4 Quadratic Functions Objectives: To graph quadratic functions

3. Graphs of Quadratic Functions Using a graphing calculator, graph the equation y = x 2. What is the lowest point on the graph? Which axis divides the graph in half? (0,0) y-axis Using a graphing calculator, graph each of the following equations. y = 2x 2 y = 2x 2 + 1 y = 2x 2 – 4x

4. Quadratic Function A function f defined by an equation of the form y = ax 2 + bx + c, where a,b, and c are real numbers and a = 0, is a quadratic function and can be written f(x) = ax 2 + bx + c. The graph of a quadratic function is called a parabola.

5. Example 1 Graph the quadratic function f(x) = -x 2. f(x) = -x 2 xf(x) -2 0 1 2 -4 0 -4 x y

6. Example 1 Graph the quadratic function f(x) = -x 2. x y The vertex is the maximum or minimum point of a parabola. vertex If the graph of a parabola is folded so that the two sides of the parabola coincide, then the fold line is the axis of symmetry. axis of symmetry

7. Vertex and Axis of Symmetry For a parabola defined by the equation y = ax 2 + bx + c: 1)the x-coordinate of the vertex is 2) the axis of symmetry is the line

8. Example 2 Find the vertex and axis of symmetry, then graph the quadratic function f(x) = 2x 2 - 8x + 4. x y y-coordinate of vertex: y = 2x 2 – 8x + 4 = 2(2) 2 – 8(2) + 4 = 8 – 16 + 4 = -4 vertex: (2,-4)

9. Example 2 Find the vertex and axis of symmetry, then graph the quadratic function f(x) = 2x 2 - 8x + 4. x y axis of symmetry: x = 2 f(x) = 2x 2 – 8x + 4 xf(x) 0 1 2 3 4 4 -2 -4 -2 4

10. Practice Find the vertex and axis of symmetry, then graph the function. 1) f(x) = -2x 2 + 4x + 1 2) g(x) = x 2 -3x + 1

11. Homework p.554-555 #1-19 odds