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QUADTRATIC RELATIONS

QUADTRATIC RELATIONS. X and Y Intercepts. X versus Y intercepts. (0, y) (x, 0). EXAMPLE:. Find the y intercept of y=5x 2 + 2x – 4 Solution: Substitute x=0 y= 5(0) 2 + 2(0) – 4 = - 4. ∴ , the coordinates of the y-intercept are (0, -4). (0, y).

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QUADTRATIC RELATIONS

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  1. QUADTRATIC RELATIONS X and Y Intercepts

  2. X versus Yintercepts • (0, y) (x, 0)

  3. EXAMPLE: • Find the y intercept of y=5x2+ 2x – 4 • Solution: Substitute x=0 • y=5(0)2+ 2(0) – 4 • = - 4 ∴, the coordinates of the y-intercept are (0, -4) • (0, y) Calculate by substituting 0 for y First number is 0

  4. Y-intercept Where it touches the y-axis • 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) Calculate by substituting 0 for y First number is 0

  5. EXAMPLE: • Find the y intercept of y=5x2+ 2x – 4 • Solution: Substitute x=0 • y=5(0)2+ 2(0) – 4 • = - 4 ∴, the coordinates of the y-intercept are (0, -4) • (0, y) Calculate by substituting 0 for y First number is 0

  6. x-intercept (aka “zeros”) Where it touches the x-axis • 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. QUADRATIC FORMULA • (x, 0) Calculate by using the above formula The second number is 0

  7. x-intercept (aka “zeros”) Where it touches the x-axis • 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

  8. Example: Find the x-intercepts for y= 2x2+ 5x -1 Recall: For quadratic equation ax2 + bx + c = 0, the solutions to a quadratic equation are given by Identify a, b, and c in ax2 + bx + c = 0: a = b = c = 2 -1 5 Now evaluate the quadratic formula at the identified values of a, b, and c

  9. 2 x-intercepts • (0.186, 0) • (-2.686, 0)

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

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