Finding zeros of a quadratic function

1. FINDING ZEROS OF A QUADRATIC FUNCTION f(x) = ax 2 +bx+c

2. Roots , Zeros , and x-intercepts of Quadratic Functions

3. The roots of a quadratic equation tell you where the graph of the function crosses the x-axis. The roots are called the x-intercepts of the graph. They correspond to points on the graph that have y-coordinates of 0. That is why the roots are also called the zeros of the quadratic function.

4. Example 1 Find the zeros of a quadratic function f(x) = x 2 +3x+2

5. f(x) = x 2 +3x+2 x 2 +3x+2 = 0 (x+2) (x+1) = 0 x+2=0 x+1=0 x= -2 x= -1 Therefore, the zeros are -2 and -1

6. Example 2 Find the zeros of a quadratic function f(x) = x 2 -5x+6

7. f(x) = x 2 -5x+6 x 2 -5x+6 = 0 (x-3) (x-2) = 0 x-3 =0 x-2=0 x= 3 x= 2 Therefore, the zeros are 3 and 2

8. What are the solutions of the quadratic equation f(x) = x 2 -2x-3

9. f(x) = x 2 -2x-3 x 2 -2x-3 = 0 (x-3) (x+1) = 0 x-3 =0 x+1=0 x= 3 x= -1 Therefore, the solutions are 3 and -1

10. Find the zeros of the ff. Quadratic Functions. F(x) = x 2 - 5x – 24 F(x) = x 2 – 2x -8 F(x) = x 2 + x – 2 F(x) = 3x 2 + 9x – 12 F(x) = 2x 2 + 15x - 8

11. Assignment: Find the zeros of the ff. Quadratic Functions. F(x) = x 2 – 3x - 4 F(x) = x 2 +5x - 6 F(x) = 6x 2 -9x - 15 F(x) = x 2 - 100 F(x) = 81x 2 – 90x + 25