1. Lesson 8-1 :Identifying Quadratic Functions Lesson 8-2 Characteristics of Quadratic Functions Obj: The student will be able to 1) Identify quadratic functions and determine whether they have a minimum or maximum 2) Graph a quadratic function and give its domain and range 1) Find the zeros of a quadratic function from its graph 2) Find the axis of symmetry and the vertex of a parabola HWK: Worksheet

2. Vocab: 1)quadratic function – any function that can be written in the standard form y = ax² + bx + c where a, b, and c are real numbers and a ≠ 0 2)parabola – the graph of a quadratic function, it is a curve 3)vertex – the highest or lowest point on a parabola 4)minimum – the y-value of the lowest point on the graph of a function – the function opens upward 5)maximum – the y-value of the highest point on the graph of a function – the function opens downward 6)zero of a function- an x-value that makes the function equal to 0 7)axis of symmetry – a vertical line that divides a parabola into two symmetrical halves

3. Tell whether each function is quadratic. Explain Ex 1) {(-2,4), (-1,1), (0,0), (1,1), (2,4)} Ex 2) y + x = 2x²

4. Graph each quadratic function using a table of values. Ex 3) y = x² + 6x + 9 xy = x² + 6x + 9y 00² + 2 = 0 + 22 11² + 2 = 1 + 23 22² + 2 = 4 + 26 (-1)² + 2 = 1 + 23 -2(-2)² + 2 = 4 + 26

5. Ex 4) y = -3x² + 1 xy = -3x² + 1y 0-3(0)² + 1 = -3(0) +1 = 0 + 1 1 1-3(1)² + 1 = -3(1) + 1 = -3 + 1 -2 2-3(2)² + 1 = -3(4) + 1 = -12 + 1 -11 -3(-1)² + 1 = -3(1) + 1 = -3 + 1 -2 -3(-2)² + 1 = -3(4) + 1 = -12 + 1 -11

6. What do you notice about the graph of the parabola a)When a > 0? b)When a < 0?

7. Minimum and Maximum Values If a > 0, the parabola opens upward, and the y-value of the vertex is the minimum value of the function. If a < 0, the parabola opens downward and the y-value of the vertex is the maximum value of the function.

8. Find the vertex, minimum or maximum, domain and range, axis of symmetry and zeros of the function Ex 5)

9. Ex 6)

10. Ex 7)

14. Find the axis of symmetry and the vertex of the graph Ex 8) y = x² - 4x – 10

15. Ex 9) y = -x² + 4x

16. Ex 10) The height above water level of a curved arch support for a bridge can be modeled by f(x) = -0.007x² + 0.84x + 0.8 where x is the distance in feet from where the arch support enters the water. Can a sailboat that is 24 feet tall pass under the bridge? Explain.