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Families of Quadratics

Families of Quadratics. Examples of Families. Here is a family of quadratic functions with the same vertex but different "a" values. Notice the all have the same axis of symmetry. More Examples. What makes this a family?

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Families of Quadratics

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  1. Families of Quadratics

  2. Examples of Families Here is a family of quadratic functions with the same vertex but different "a" values. Notice the all have the same axis of symmetry

  3. More Examples What makes this a family? It is the fact that each parabola has the same x intercepts and the same axis of symmetry. The only thing that is different is the "a" values.

  4. One last example What makes this a family of quadratics? You guessed it! They all have the same y intercepts So in conclusion, there are more than one ways that a parabola can be part of a family.

  5. Some questions…… • Determine the equation of the parabola with x intercepts of –4 and 3 that passes through (2,7)

  6. Another one!…..you should know this by now!! • Determine the equation of the parabola with the vertex (-2,5) through (4,-8)

  7. What about a word problem. Work in pairs to try and solve this. • A tunnel with a parabolic arch is 12m wide. If the height of the arch 4 meters from the left edge is 6m, can a truck that is 5 m tall and 3.5 m wide pass through the tunnel

  8. (-2,6) (-6,0) (6,0) What to do? Set up a diagram. Look for the a value then find the equation.

  9. Keep Going Next find the x coord of the vertex: Plug this into equation:

  10. (-2,6) (-6,0) (6,0) Almost there! So the bridge will be high enough in the middle. Now since the truck is 3.5 m wide that means that the parabola must be above the point (3.5, 5). So plug in 3.5 for x and solve for y! (0,5) (1.75,5) (-1.75,5) (0,0)

  11. The truck can go under because 3.5 m from the centre the bridge is 6.17 m high and the truck is 5 m high. In conclusion

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