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Sketching parabolas
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- 2. What is tobe Learned? • How to sketch a parabola – Showing roots – And Turning points Not Yet!
- 3. Turning Points y =x2 – 2x – 15 Complete the square = (x – 1)2 – 1 – 15 = (x – 1)2 – 16 Min Value of y = - 16, when x = 1 i.e Min Turning Point (1 , -16)
- 4. Very Handy For y= x2 – 2x – 15 Must be Minimum Turning Point (1 , -16)
- 5. y = x2 +6x + 4 Complete the square = (x + 3)2 – 9 + 4 = (x + 3)2 – 5 Min Value of y = -5, when x = -3 i.e Min Turning Point (-3, -5) Minimum Turning Point (-3, -5)
- 6. Roots Occur where curvecuts x axis Where y = 0 Roots Turning Point
- 7. Minimum Turning Point (1, -16) y = x2 – 2x – 15
- 8. Finding Roots y =x2 – 2x – 15 For Roots y = 0 = x2 – 2x – 15 or x2 – 2x – 15 = 0 (x – 5)(x + 3) = 0 x – 5 = 0 or x + 3 = 0 x = 5 x = -3 Coordinates of Roots (5 , 0) and (-3 , 0) y0 (1 , -16) y = x2 – 2x – 15
- 9. Finding Roots y =x2 – 4x For Roots y = 0 = x2 – 4x or x2 – 4x = 0 x(x – 4) = 0 x = 0 or x – 4 = 0 x = 0 x = 4 Coordinates of Roots (0 , 0) and (4 , 0) y0
- 10. Finding Y Intercept VeryEasy Occurs where x = 0 y = x2 – 2x – 15 X= 0 y = 02 – 2(0) – 15 = -15 Y Intercept (0 , -15)
- 11. Sketching Parabolas Vital Pointsand Tactics • Roots (y = 0) • Y Intercept (x = 0) • Turning point (complete square)
- 12. Ex y =x2 + 6x + 8 Roots (y = 0) x2 + 6x + 8 = 0 Factorising (x + 4)(x + 2) = 0 x + 4 =0 or x + 2 =0 x = -4 or x = -2 Roots (-4 , 0) and (-2 , 0) Y Intercept (x = 0) v = 02 + 6(0) + 8 = 8 Y intercept (0 , 8)
- 13. Turning point (completeSquare) y = x2 + 6x + 8 = (x + 3)2 – 9 + 8 = (x + 3)2 – 1 Min Value, y = -1, when x = -3 Min Turning Point (-3, -1) Shape Positive
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- 15. x y 6 1 5 (3, -4) KeyQuestion Sketch y =x2 – 6x + 5 showing turning point, roots and y intercept