1. QUADTRATIC RELATIONS X and Y Intercepts

2. (0, y)(x, 0)

3. EXAMPLE: Find the y intercept of y=5x 2 + 2x – 4 Solution: Substitute x=0 y= 5(0) 2 + 2(0) – 4 = - 4 (0, y) First number is 0 Calculate by substituting 0 for y ∴, the coordinates of the y-intercept are (0, -4)

4. To find the y intercept, the x coordinate is 0 and the y coordinate is found by substituting 0 for x in the relation and calculating the value for y. (0, y) First number is 0 Calculate by substituting 0 for y Where it touches the y-axis

5. EXAMPLE: Find the y intercept of y=5x 2 + 2x – 4 Solution: Substitute x=0 y= 5(0) 2 + 2(0) – 4 = - 4 (0, y) First number is 0 Calculate by substituting 0 for y ∴, the coordinates of the y-intercept are (0, -4)

6. To find the x intercept, the y coordinate is 0 and the x coordinate is found by substituting the values for a, b and c into the equation below, and then calculate x. (x, 0) Calculate by using the above formula The second number is 0 QUADRATIC FORMULA Where it touches the x-axis

7. So the quadratic formula is used to find the x-intercepts. There can be 2, 1 or no x-intercepts. (x, 0) Calculate by using the above formula The second number is 0 Where it touches the x-axis

8. Example: Find the x-intercepts for y= 2x 2 + 5x -1 Recall: For quadratic equation ax 2 + bx + c = 0, the solutions to a quadratic equation are given by Identify a, b, and c in ax 2 + bx + c = 0: a = b = c =2 5 Now evaluate the quadratic formula at the identified values of a, b, and c

9. (0.186, 0) (-2.686, 0)

10. X-INTERCEPTS COMPLETE QUESTION 13 (14 is homework) Find the x-intercepts if any!